Mac and Tosh are resting on top of the water near the end of the pool when Mac creates a surface wave. The wave travels the length of the pool and back in 25 seconds. The pool is 25 meters long. Determine the speed of the wave.

Answer:

Step-by-step explanation:

The price of the car before tax was $18,560.3

Let the price of the car be x. Then,

x + 6% of x = $19,674

106x/100 = $19,674

x = $ 19,673*100/106

with BODMAS, we get

x= $18560.3

To know more about %, click on the link below:

https://brainly.com/question/24877689

The slopes and the y-intercepts of two equations are different.

Mathematically, the slope-intercept form of a line can be calculated by using this equation:

y = mx + c

Where:

From the information provided, we have the following equations:

2x + y = 3       ....equation 1.

−2y = 14 − 6x    ....equation 2.

In slope-intercept form, the first equation can be written by subtracting 2x from both sides as follows:

2x + y - 2x = 3 - 2x

y = 3 - 2x

y = -2x + 3

Therefore, m = -2 and c = 3.

For the second equation, we would divide both sides by -2 as follows:

−2y/-2 = 14/-2 − 6x/-2

y = -7 + 3x

y = 3x - 7

Therefore, m = 3 and c = -7.

In this context, we can reasonably and logically deduce that the slopes and the y-intercepts are quite different.

Read more on slope here: brainly.com/question/14345501

#SPJ1

Answer:

y = -2x + 3

y = 3x + -7

The slopes and the y-intercepts are different.

The system represents lines that Intersect at one point

Exactly one solution

Step-by-step explanation:

Edge2022

get me brainliest

The slope of the function A which is presented as an equation and the slope of function B presented as a table are presented as follows;

The slope of function A is 4

The slope of function B are;

Between f(0) and f(1), the slope is 1

Between f(1) and f(2), the slope is 3

Between f(2) and f(3), the slope is 5

The slope is found by the ratio of the rise to the run of the graph.

The function A is; y = 4·x - 5

Function A is of the form y = m·x + c

Where;

m = The slope of the function = 4

Therefore;

The slope of function A is 4

The first difference of the values of function B is not a constant.

The value of f(0) in function B is 0

The value of f(1) in function B is 1

The slope between f(0) and f(1) is m = (f(1) - f(0))/(1 - 0)

Which indicates that m = (1 - 0)/(1 - 0) = 1

The slope of function B between f(1) and f(2) is found as follows;

f(2) = 4, f(1) = 1, from which we get;

m = (4 - 1)/(2 - 1) = 3

The slope between f(2) and f(1) is 3

The slope of the function B between f(2) and f(3) is found as follows;

f(2) = 4, f(3) = 9, from which we get;

m = (9 - 4)/(3 - 2) = 5

The slope of the function B between f(2) and f(3) is 5

Learn more about the average slope of a curve here:

https://brainly.com/question/19376563

#SPJ1

When a quadratic equation is given in the form y = a( x− ℎ )^2 + k the easily seen features are

Equation of a parabola is the equation used to trace the path of a parabola. this equation is a quadratic equation

The quadratic equation in the factored form is written as

y = a ( x − ℎ )^2 + k

This equation shows the coordinates of the vertex which is v(h, k)

The axis of symmetry refers to the axis where the parabolic curve can be bisected. this is in the y axis

"a" helps to determine if the curve opens upwards or downwards. when a is:

Learn more about factored form of quadratic equation here:

https://brainly.com/question/29339843

#SPJ1

The expected value of your third punch is 5660.

What is probability?

A linear scale from 0 (impossibility) to 1 (certainty) or as a percentage between 0 and 100% expresses the likelihood that a specific event (or series of events) will occur.

Given that,

This is the third and last punch and also there is no removal of prizes after each punch. Hence, the expected value would be equal to the mean of all the possibilities available.

E(third punch) = Σ  x  p(x)

=  100× (5/50) + 250 × (10/50) + 500 × (10/50) + 1000 × (10/50) + 2500 ×(8/50) + 5000 × (4/50)     + 100000 × (2/50) + 25000 × (1/50)

=  5660

Let us find the median of the given possibilities,

5 100's, 10 250's, 10 500's, 10 1000's, 8 2500's, 4 5000's, 2 100000's, 1 25000

There is a total of 50 possibilities and hence the median will be the average of the 25th and 26th terms.

25th term = 500

26th term = 1000

Median = (500 + 1000) / 2 = 750

The next available possibility greater than 750 is 1000.

Probability of getting more than 1000 in third punch = P (x > 1000) = (No. of terms greater than 1000) / Total no. of possible outcomes                                                                                                         = 15 / 50 = 0.3

Probability of getting less than 1000 in third punch = P (x > 1000) = (No. of terms lesser than 1000) / Total no. of possible outcomes                                                                                                                

= 25 / 50 = 0.5

Hence, in the second chance of punch, 1000 or anything greater than 1000 is preferred because the probability of getting more than 1000 in the next chance is less than the probability of getting less than 1000.

To learn more about the probability from the given link

https://brainly.com/question/25870256

#SPJ1

Answer:

The costs are equal at 3 miles.  It coest $8 for either company

At 8 miles the green cost 13 and the red cost 18.

My advice would be to use the Red compnay if traveling less than 3 miles and the green company is traveling more than 3 miels.  At 3 miles the costs are the same.

Step-by-step explanation:

Answer: (3, 1)

Step-by-step explanation:

Plug in each coordinate and see if the equation holds true:   

[tex](13, 2)\\13+2(7)=13+14=27\neq 10[/tex]

[tex](2, 1)\\2+7(1)=2+7=9\neq 10[/tex]

[tex](4, 1)\\4+7(1)=4+7=11\neq 10[/tex]

[tex]3+7(1)=3+7=10[/tex]

Step-by-step explanation:

x = price per muffin

21 × x = 30

x = 30/21 = 10/7 = $1.428571429... ≈

≈ $1.43

she needs to charge $1.43 per muffin.

The dimensions that will minimize the cost, obtained from the cost function are;

Width = [tex]\sqrt[3]{\frac{45}{11} }[/tex] feet

Length = [tex]2\cdot \sqrt[3]{\frac{45}{11} }[/tex] feet

Height = [tex]\dfrac{20}{\left(\sqrt[3]{\frac{45}{11} }\right)^2 }[/tex]

A function is a rule, or law or expression that provides the definition between an input variable and an output variable.

Base length of the box = 2 × The base width of the box

Cost of the material used to build the top and the bottom = $11 per square feet

Cost of the material used to build the sides = $3 per square feet

Volume of the box = 40 cubic feet

Let x represent the width of the base of the box, and let y represent the height of the box

The information from the question indicates;

The length of the base of the box = 2·x

The volume of the box, V = x × 2·x × y = 2·x²·y = 40

V = 2·x²·y = 40

[tex]y = \dfrac{40}{2\cdot x^2} = \dfrac{20}{x^2}[/tex]

The cost of the box which can be obtained from the surface area of the box can be found as follows;

Cost of the top and the bottom = 2 × x × 2·x × 11 = 44·x²

Cost of the material for the sides = (2 × x × y + 2 × 2·x × y) × 3 = 18·x·y

Cost of the box, C = 44·x² + 18·x·y

[tex]C = 44\cdot x^2 + 18\cdot x \times \dfrac{20}{x^2} = \dfrac{44\cdot x^2+360}{x}[/tex]

To minimize the cost of the box, we get;

[tex]C' =\dfrac{d}{dx}\left( \dfrac{44\cdot x^2+360}{x}\right) = 0[/tex]

[tex]\dfrac{d}{dx}\left( \dfrac{44\cdot x^3+360}{x}\right) = \dfrac{x\times 44\times 3 \times x^2 - \left(44\times x^3+360\right)}{x^2} = \dfrac{88\cdot x^3-360}{x^2} =0[/tex]

At the minimum cost, [tex]\dfrac{88\cdot x^3-360}{x^2} =0[/tex]

Therefore; 88·x³ - 360 = 0

88·x³ = 360

[tex]x = \sqrt[3]{\dfrac{360}{88} } =\sqrt[3]{\dfrac{45}{11} }[/tex]

The width of the base of the box that minimizes the cost is; [tex]x =\sqrt[3]{\dfrac{45}{11}}[/tex]

The length of the base of the box that minimizes the cost is; [tex]2\cdot x =2\times \sqrt[3]{\dfrac{45}{11}}[/tex]

The height of the box that minimizes the cost is; [tex]\dfrac{20}{x^2} = \dfrac{20}{\sqrt[3]{\dfrac{45}{11} } }[/tex]

Learn more about the minimum value of a function here:

https://brainly.com/question/24065590

#SPJ1

The most equitable way to share the coin between Mai and Jeff is ratio 5:3. Mai will have 5 coins and Jeff 3 coins

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. The general form of representing a ratio of between two quantities say 'a' and 'b' is a: b.

Mai dropped 5 loaves and Jeff 3 loaves. This means that the ratio of brad dropped by Mia and Jeff is 5:3.

The stranger dropped 8coins. the most equitable way to share the coin is to share it in ratio 5:8

Using this ratio, the total ratio is 8

therefore Mia will have 5/8×8=5coins

Jeff will have 3/8×8= 3coins

learn more about ratio from

https://brainly.com/question/2328454

#SPJ1

Answer: unit rate

Step-by-step explanation:

its obvious

Answer:

I believe it is a unit rate

Answer:

[tex]-1.7f+-25[/tex]

Step-by-step explanation:

1 ) To simplify combine like terms...

[tex]=-2.5f+0.8f+-16+-9[/tex]

[tex]=(-2.5f+0.8f)+(-16+-9)[/tex]

[tex]=-1.7f+-25[/tex]

Hope this helps! :)

We can find the linear equation by using the given graph, the equation is:

y = 4.8*x + 24

On the graph we can see the best fit line, remember that a linear equation is of the form:

y = m*x + b

Where m is the slope and b is the y-intercept.

On the graph we can see that the y-intercept is at y = 24, then:

y = m*x + 24

Now, notice that when x = 5, the value of y is 48, replacing these values we get:

48 = m*5 + 24

48 -24 = m*5

24/5 = m

4.8*m

The linear equation is:

y = 4.8*x + 24

Learn more about linear equations:

https://brainly.com/question/1884491

#SPJ1

The polynomial f(c)=4x^3+19x^2-58x+35 as a product of linear factors is f(c)=(x-1)(x+7)(4x-5)

To express the polynomial as a product of linear factors we have to find the zeros of the polynomial.

Here,

We have Given that f(c)=4x^3+19x^2-58x+35 and -7 is a zero of f(k) and we need to find the polynomial f(c)=4x^3+19x^2-58x+35 as a product of linear factor

Now,

-7 is a zero of f(k)

i.e. (x+7) is a linear factor of f(k)

now,

we will find out the linear factor of f(c)

so,

f(c)=4x^3+19x^2-58x+35

f(c)=4x^3-4x^2+23x^2-23x-35x+35

f(c)=(x-1)(4x^2+23x-35)

f(c)=(x-1)(4x^2+28x-5x-35)

f(c)=(x-1)(4x(x+7)-5(x+7))

f(c)=(x-1)(x+7)(4x-5)

Hence,

The polynomial f(c)=4x^3+19x^2-58x+35 as a product of linear factor is f(c)=(x-1)(x+7)(4x-5)

Thus,

the linear factor of given polynomial is (x-1)(x+7)(4x-5)

to learn more about linear factor of polynomial refer to :

https://brainly.com/question/26791528

#SPJ1

According to the given distance, the dog can run on 22.5 miles

Distance:

Distance refers the the length of the line joining the two points. Here the two points lie on the same horizontal or same vertical line, the distance can be found by subtracting the coordinates that are not the same.

Given,

On his trip to meet Clare, Kiran brought his dog with him.

Here at the same time Kiran and Clare started walking, the dog started running 6 miles per hour.

When they got to Clare it turned around and ran back to Kiran. And when it got to Kiran, it turned around and ran back to Clare, and continued running in this fashion until Kiran and Clare met.

Here we know that they meet after 3.75 hours.

And we know that the dog was running 6 miles per hour

So, for 3.75 hours, it can be calculated as,

=> 3.75 x 6

=> 22.5

Therefore, then the dog can ran 22.5 miles.

To know more about Distance here.

https://brainly.com/question/15256256

#SPJ1

The customer have to pay $87.9 for the watch.

A customer at the store wanted to buy a different watch that was listed at $88 but had a 15% discount.

Given the information is

Watch is listed at $88 and had a discount of 15%

The customer had to pay a sales tax of 5%

Than, by reducing the discount from the price listed

= $88 - 15%

= 88 - [tex]\frac{15}{100}[/tex]

= 87.85

Now we have to add 5% tax to the discounted price

= 87.85+5%

= $87.9

Hence the answer is the customer have to pay $87.9 for the watch.

To learn more about discounts click here https://brainly.com/question/7459025

#SPJ9

The observation I can make of the pattern is that the sequence always increase by 10.

The sequence above shows an arithmetic pattern. Therefore, the arithmetic formula can be used to solve the next sequence.

7, 17, 27, 37, 47, 57..

Therefore,

aₙ = a + (n - 1)d

where

Therefore,

a = 7

d = 17 - 7 = 10

Hence, the arithmetic formula is as follows:

aₙ = 7 + (n - 1)10

aₙ = 7 + 10n - 10

aₙ = 10n - 3

The sequence always increase by 10.

learn more on arithmetic sequence here:https://brainly.com/question/14013716

#SPJ1

The polynomial function with -3 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1 will be x³+9x²+16x.

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

It is given that the polynomial is given with -3 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1.

Each zero, such as a, corresponds to a linear factor, such as (x a). The repeating of such components is corresponding to multiplicity. The following polynomial thus meets the requirements in our example:

= (x-(-3))³(x-0)¹

=(x³-3x²(-3)+3x(-3)²-(-3)²)(x)

=x³+9x²+27x-9x

=x³+9x²+16x

Thus, the polynomial function with -3 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1 will be x³+9x²+16x.

Learn more about Polynomial here:

brainly.com/question/17822016

#SPJ1

If you want easy access to your money for paying bills, eating out, etc, it is best to use a checking account.

A checking account is a sort of bank account that enables simple deposits and withdrawals of cash for everyday use.

For instance, you may use your debit card to withdraw cash, deposit a check you receive, or set up direct deposit to get your paychecks.

It is advisable to utilize a checking account if you want quick access to your money for things like paying bills and dining out.

Learn more on checking account here:

https://brainly.com/question/26181559

#SPJ1

The previous population of the city is 62500

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 3x + 4y = 14, 5x − 4y = 4.

if the previous population is represented by x and the increment by y, then

y= x×28/100

y = 28x/100 equation 1

the new population = previous population+ increment

therefore x+y= 80,000

represent 28x/100 for y in equation 2

x+28x/100= 80000

making the LHS a single fraction

(100x+28x)/100= 80000

128x= 80000×100

divide both sides by 128

x= 8000000/128

x= 62500

therefore the previous population is 62500

learn more about Simultaneous equation from

https://brainly.com/question/16863577

#SPJ1

The equation of the given line is y = 2x + 4

The equation y = mx + c is the general equation of any straight line, where m is the slope of the line and c is the y -intercept.

Given a line passing through points (-1, 2) and (-3, -2)

We know (y - y1) = [(y2−y1)/(x2−x1)](x - x1).

Therefore, y - 2 = [(-2-2)/(-3+1)](x+1)

y-2 = 2x + 2

y = 2x + 4

Hence, The equation of the given line is y = 2x + 4

For more references on the equation of a line, click;

https://brainly.com/question/21511618

#SPJ1

The value of expression a²-b is 12 and value of equation -a+√-4+b id 10+2i where a is -2 and b is 8.

In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression in mathematics is a collection of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) Expressions and phrases are similar in structure.

Here,

if a = -2 and b = 8

a²-b=(-2)²-8

=-4

-a+√-4+b=-(-2)+2i+8

=10+2i

The equation a²-b has a value of 12 and the expression -a+-4+b has a value of 10+2i, where a is -2 and b is 8.

To know more about expression,

https://brainly.com/question/14961928?referrer=searchResults

#SPJ1

Answer:

1,200 pennies

Step-by-step explanation:

The linear equation in the slope intercept form that models this situation is y = 9x + 15 .

In the question ,

it is given that ,

a member of hiking club paid $51 for 4 months ,

let the number of months be represented on x coordinate , and

the amount paid be represented on y coordinate .

So , the point becomes (4 , 51).

also given that you pay a total of $105 after 10 months ,

the second point becomes (10 , 105).

to find the equation in slope intercept form , we need slope ,

So , Slope = (105-51)/(10-4)

= 54/6

= 9

So , the equation having the point (4,51) and slope as 9 , in slope intercept form is

(y - 51) = 9(x - 4)

y - 51 = 9x - 36

y = 9x - 36 + 51

y = 9x + 15

Therefore , The linear equation in the slope intercept form that models this situation is y = 9x + 15 .

Learn more about Slope Intercept Form here

https://brainly.com/question/9682526

#SPJ1

Answer:

12 pints

Step-by-step explanation:

[tex]\frac{1}{8}[/tex] = [tex]\frac{8}{96}[/tex]

8 ounces is equal to 1 pint.  8 x 12 = 96, so 1 x 12 is 12

If no withdrawals were made from the accounts. The total interest earned at the end of 1 year is $230 and the percent interest for the total deposited is 5.75%.

a. Total interest earned  :

Total interest earned  = (0.02)($1000)+(0.07)($3000)

Total interest earned =$20+$210

Total interest earned =$230

b. Percent interest amount deposited

Percent interest amount deposited = Total interest earned / Total amount deposited

Percent interest amount deposited = $230 /( $1,000 + $3,000)

Percent interest amount deposited = $230 / $4000

Percent interest amount deposited = 0.0575 × 100

Percent interest amount deposited =5.75%

Therefore $230 is the interest earned and 5.75 is the percent interest.

Learn more about total interest earned here:https://brainly.com/question/25296782

#SPJ1

Answer:

7.1032,7.209,7.23,7.3.

so we can not put the dot and imagine like 71032 72090 we not put the 0 but it's can not be with no 0 72300 and we not put 0 73000 it most greatest so

i write answer on the top!

The overall weighted average grade for this student in the class is 83.5%.

The weighted average grade is a function of the multiplication of each rate by the average score for each grading category.

The class grades are added to obtain the total grade that the student received for the different categories, involving class participation, classwork/homework, and tests/projects.

                                      Grade   Average    Class Grade

Participation                    10%        100          10% (10% x 100%)

Classwork/Homework   30%         95          28.5% (30% x 95%)

Test/projects                  60%         75          45% (60% x 75%)

Total grade in class                                      83.5%

Thus, from the student's participation, classwork/homework, and tests/projects, we can summarize that they scored an average weighted grade of 83.5%.

Learn more about the weighted average at https://brainly.com/question/24398353

#SPJ1

115.5  is the total amount of interest paid by this investment at the end of 5 years

What is the Percentage?

percentage, a relative value indicating the hundredth parts of any quantity.

Given,

Samantha invested $660 into an account that paid 3.5% interest compounded annually.

We need to find the total amount of interest paid by this investment at the end of 5 years

A=P(1+rt)

A is the final amount

P is the principal amount

r is the rate of interest

t is time

A=?,P=660,r=3.5%=0.035, t=5

A=660(1+0.035(5))

=660(1+0.175)

=660(1.175)

A=775.5

To check the total amount of interest paid by this investment at the end of 5 years

We need to find the difference between the initial amount and the final amount

775.5-660 =115.5

Hence 115.5  is the total amount of interest paid by this investment at the end of 5 years

To learn more about Percentage  from the given link

brainly.com/question/28269290

#SPJ1