Trisha and Byron are washing and vacuuming cars to raise money for a class trip. Trisha raised $38 by washing
5 cars and vacuuming 4 cars. Byron raised $28 by washing 4 cars and vacuuming 2 cars. Find the amount they
charged to wash a car and vacuum a car.

a. Sean drank at a rate of 5 milliliters per second.

b. It took Sean 55 s to drink all the slushy.

Since Sean darnak at a constant rate and originally there were 275 milliliters of slushy in the cup. After 13 seconds, 210 milliliters of slushy remained.

The rate at which Sean drank, r = Change in volume of slushy/time for change

= (275 mL - 210 mL)/13 s

= 65 mL/13 s

= 5 mL/s

So, Sean drank at a rate of 5 milliliters per second.

The time it takes Sean to drink all the slushy is given by

T = V/r where

So, T = V/r

= 275 mL/5 mL/s

= 55 s

So, it took Sean 55 s to drink all the slushy.

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The equivalent quotient of the expression √16/√8 are: √2 and √4 / √2

We want to find the equivalent quotient of the given expression; √16 / √8

Now, we know that the square root of 16 is equal to 4 i.e. √16 = 4

Thus, applying that to our expression gives;

√16/√8 = 4/√8

Now, square root of 8 which is √8 can also be expressed as; 2√2

Thus;

4/√8  = 4/2√2 = 2/√2

The steps to rationalize the denominator, to get rid of all radicals that are in the denominator are as follows;

Step 1: Multiply numerator and denominator by a radical that will get rid of the radical in the denominator.

Step 2: Make sure all radicals are simplified.

Step 3: Simplify the fraction if needed.

If we rationalize the denominator of our expression, we have;

2/√2 × √2/√2 = 2√2/ 2 = √2

Also, 2/√2 can be expressed as √4 /√2

Therefore, The equivalent quotient of the expression √16/√8 are: √2 and √4 / √2

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Answer:

2.78%

Step-by-step explanation:

Probability Formula

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

We are told that the six-sided dice is fair. This means that each of the faces has the same probability of being rolled.

Therefore, the probability of rolling one is:

[tex]\implies \sf P(x = 1)=\dfrac{1}{6}[/tex]

The probability of rolling six is:

[tex]\implies \sf P(x = 6)=\dfrac{1}{6}[/tex]

Therefore, the probability of rolling one and then six is:

[tex]\begin{aligned}\implies \sf P(x=1)\:and\:P(x=6) & = \sf \dfrac{1}{6} \times \dfrac{1}{6}\\& =\sf \dfrac{1}{36}\\& = \sf 0.0278\:(3\:s.f.)\\& = \sf 2.78\%\:(3\:s.f.)\end{aligned}[/tex]

Total elements in sample space=6

P(1)

P(6)

P(1 and 6)

Answer:

110

Step-by-step explanation:

10w + 4x

10 (9) + 4 (5)

90 + 20

110

The answer is 110.

Hope it helps!

Have a nice day:)

[tex]\textbf{Heya !}[/tex]

the mode is the number that occurs the most

All numbers here occur once, except [tex]\sf{100}[/tex].

so 100 is the mode.

`hope it was helpful to u ~

A year later, Mia gained $400.

Mia invests in an index fund= $5000

The share price of the fund has grown by 8% after a year.

So, one year later Mia's investment would also increase by 8% since her invested share value has grown by 8%.

Hence, the amount of share would be = ($5000 + 8% of $5000) =($5000+$5000*8/100) = ($5000+$400) = $ 5400

Therefore, Mia's gain is $400.

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Answer: 12

Step-by-step explanation:

Let's say that the length needed to be found is x
As the two lengths of both triangles are parallel to one another, we can use the equation to find x
6/x = (6+4)/20

6/x = 1/2

x = 12

Using a system of equations, it is found that there are 147 dimes and 52 quarters in the machine.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

There are 199 coins, hence:

x + y = 199 -> y = 199 - x.

The value of dimes(each is worth $0.1) is $1.7 more than the sum of the quarters(each is worth $0.25), hence:

0.1x - 0.25y = 1.7.

Since y = 199 - x:

0.1x - 0.25(199 - x) = 1.7.

0.35x = 51.45

x = 51.45/0.35

x = 147

y = 199 - 147 = 52

There are 147 dimes and 52 quarters in the machine.

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The value of x= 20 units

BD =  BF

BD =2x + 40

BF = 18x

Equate the expressions thus:

2x + 40 = 2/3(18x)

2x + 40 = 12x

Collect like terms

2x - 12x = - 40

-2x = - 40

Divide both sides by - 2

x = 20

Hence, x =  20 units

The centroid is the center point of the item. The factor in which the 3 medians of the triangle intersect is known as the centroid of a triangle. it is also defined because of the point of intersection of all the 3 medians. The median is a line that joins the midpoint of a facet and the opposite vertex of the triangle.

Then, we can calculate the centroid of the triangle by means of taking the common of the x coordinates and the y coordinates of all of the three vertices. So, the centroid method can be mathematically expressed as G(x, y) = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/three).

The centroid of a triangle is the point at which the 3 medians coincide. The centroid theorem states that the centroid is 23 of the space from each vertex to the midpoint of the opposite aspect.

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Answer:

(っ◔◡◔)っ ♥ 36 square root 2 ♥

Step-by-step explanation:

The length of the hypotenuse of the triangle is approximately 48.99 units.

Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We can apply this theorem only in a right triangle.

Example:

The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.

Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm

We have,

We can use the Pythagorean theorem to find the length of the hypotenuse of the triangle:

c² = a² + b²

where c is the length of the hypotenuse, and a and b are the lengths of the legs.

Substituting the values given in the problem.

c² = 18² + 36²

c² = 324 + 1296

c² = 1620

Taking the square root of both sides.

c = √(1620)

Simplifying.

c = 6 √(90) or approximately 48.99

Therefore,

The length of the hypotenuse of the triangle is approximately 48.99 units.

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Answer:

4

Step-by-step explanation:

Question :

Solution :

⇒ 3 [-x + 2x + 1] = x - 1

⇒ 3 [x + 1] = x - 1

⇒ 3 × [x + 1] = x - 1

⇒ 3x + 3 = x - 1

⇒ 3x - x + 3 = -1

⇒ 2x + 3 = -1

⇒ 2x = -1 - 3

⇒ 2x = -4

⇒ x = -4 / 2

⇒ x = -2

Simplifying

3[-1x + (2x + 1)] = x + -1

Reorder the terms:

Remove parentheses around (1 + 2x)

Reorder the terms:

Combine like terms: -1x + 2x = 1x

Reorder the terms:

Solving

Solving for the variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1x' to each side of the equation.

Combine like terms: 3x + -1x = 2x

Combine like terms: x + -1x = 0

Add '-3' to each side of the equation.

3 + -3 + 2x = -1 + -3

Combine like terms: 3 + -3 = 0

Combine like terms: -1 + -3 = -4

Divide each side by '2'.

Simplifying

Answer:

x=7 y=3

Step-by-step explanation:

-x+6y=11

2x-3y=5

-2x+12y=22

2x-3y=5

Add both equations

-2x+2x-3y+12=22+5

9y=27

y=3

plug y back in

-x+18=11

-x=-7

x=7

Using it's formula, the present value of the amount is: $288.

The present value formula is:

[tex]PV = \frac{R}{(1 + r)^n}[/tex]

In which the parameters are:

Considering quarterly compounding, the parameters for this problem are as follows:

R = 450, r = 0.075/4 = 0.01875, n = 6 x 4 = 24.

Hence the present value is:

[tex]PV = \frac{R}{(1 + r)^n}[/tex]

[tex]PV = \frac{450}{(1.01875)^{24}}[/tex]

PV = $288

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All the relevant transformations are as shown in the explanations below.

We are given the original function as y = x and told the transformation is as follows;

1) y = x + 5; This means that the function was shifted 5 units to the left.

2) y = ³/₈x; This means that the function was vertically stretched by a scale factor of  ³/₈.

3) y = -x - 2 or y = -(x + 2); This means that the function was first shifted by 2 units to the left before being reflected over the x-axis.

4) y = 6x + 1; This means that the function was stretched by a factor of 6 and then shifted 1  unit to the left.

5) y = x - 11; This means that the function was shifted 11 units to the right.

6) y = 8x; This means that the function was vertically stretched by a scale factor of  8.

7) y = -1/3x; This means that the function was horizontally stretched by a scale factor of  1/3.

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The time for the village to dig the new well is about 7 1/2 years. At this time the population doubles from its current size.

For a function f(x) = y, the steps to draw a graph for the given function are as follows:

It is given that,

f(x) = 200 × [tex](1.098)^x[/tex]

Village's population growing rate = 9.8%

Creating a table for x and f(x) values:

x: 0   2   4   6   8   10

f(x = 0) = f(0) = 200 × [tex](1.098)^0[/tex] = 200

f(x = 2) = f(2) = 200 × [tex](1.098)^2[/tex] = 241

f(x = 4) = f(4) = 200 × [tex](1.098)^4[/tex] = 291

f(x = 6) = f(6) = 200 × [tex](1.098)^6[/tex] = 350

f(x = 8) = f(8) = 200 × [tex](1.098)^8[/tex] = 423

f(x = 10) = f(10) = 200 × [tex](1.098)^1^0[/tex] = 509

So,

(x, f(x)): (0, 200)  (2, 241)  (4, 291)  (6, 350)  (8, 423)  (10, 509)

Plotting these points in the graph and joining the points, the graph is shown below.

Finding the time for the village to dig a new well:

It is given that the population doubled from its current size, the village will need to dig new water well.

The current size of the village = 200

If it doubles for a certain time 't' = 400

So,

400 = 200 × [tex](1.098)^t[/tex]

⇒ [tex](1.098)^t[/tex] = 2

⇒ log[tex](1.098)^t[/tex] = log 2

⇒ t log(1.098) = 0.301

⇒ t × 0.04 = 0.301

∴ t = 7.525 years

Therefore, the village's population becomes double at the time 7 and half years from now. So, after 7 1/2 years, the village needs to dig a new well.

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The natural number , n is 30

Given;

GCF(n, 70) = 10

LCM(n, 70) = 210

We have that;

LCM(A,B) x GCF(A, B)= A x B

Then,

(n, 70) = n × 70 = 70n

10 × 210 = 2100

Equate the two expressions

70n = 2100

n = [tex]\frac{2100}{70}[/tex]

n = [tex]30[/tex]

Thus, the natural number , n is 30

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The polynomials are classified as follows:

Depends on the number of terms, as follows:

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Answer: 4/7

Step-by-step explanation:

You pick one black sock, meaning there are 14 socks remaining in the drawer, 8 of which are black. Thus, the probability is 8/14, which simplifies to 4/7.

Each element in a population has an equal chance of being chosen is Random selection.

Given that each element in a population has an equal chance of being chosen for inclusion in the sample independent of any other event in the process.

Sampling is an umbrella term for all methods used to take samples from populations. The main purpose of sampling is to ensure that a chosen sample reflects the desired characteristics of a population so that a statistical study can produce accurate and reasonable results. Sampling techniques include random sampling, stratified sampling and many others.

As we know, random selection is the process of selecting a small group of people from a larger group to participate in a study. Each person has an equal chance of being selected, giving each person in the group an equal chance to participate.

Hence, Each element in a population has an equal chance of being chosen for inclusion in the sample independent of any other event in the process is known as random selection.

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[tex]t \geqslant 35[/tex]

What is percentage change?

By quantifying the difference between two numbers and expressing it as an increase or decrease, the Percentage Change Calculator (percent change calculator) may determine the percentage change.

The initial price [tex]V_{1}[/tex] (100%) was decreased by 10%., then this reduced price is reduced more by 20% that becomes the final price [tex]V_{2}[/tex] which is 72.

Calculate percentage change from [tex]$V_{1}=100$[/tex] to [tex]$V_{2}=72$[/tex].

=[tex]& \frac{\left(V_{2}-V_{1}\right)}{\left|V_{1}\right|} \times 100 \\[/tex]

[tex]=& \frac{(72-100)}{|100|} \times 100 \\[/tex]

[tex]=& \frac{-28}{100} \times 100 \\[/tex]

[tex]=&-0.28 \times 100 \\[/tex]

[tex]=&-28 \% \text { change } \\[/tex]

[tex]=& 28 \% \text { decrease }[/tex]

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The graph is a decreasing exponential graph.

Part A: The given graph is decreasing the exponential graph since the graph is decreasing rapidly as the value of x is increasing the value of y is decreasing very rapidly.

Part B: The graph shown here is maybe the case of any electric appliance which is of cheap quality. The time when it is brought then its performance and its life is awesome after that its life is decreasing rapidly.

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Answer:

The answer to our question is A = 16,100(1.001)12t; $17,510

Step-by-step explanation:

I hope this helps and have a good day!

The ratio of the number of sundaes with nuts to the number of sundaes without nuts is; 11:39

We are given;

Number of sundaes with nuts sold = 11

Number of sundaes without nuts sold = 39

Thus, the ratio of the number of sundaes with nuts to the number of sundaes without nuts is;

11:39

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Answer:

106

Step-by-step explanation:

If 1 student gets a 1, and 106 get a 100, then the mean will be 99.99, and 106 students will get the extra credit.

The days of the year (excluding Sundays) paul attends school is 183 days

Months Paul skipped school = January, February, June, July August

= 31 + 28 + 30 + 31 + 31

= 151 days

Days he attend school excluding Sunday = Total days in a year - (Months Paul skipped school + Sundays)

= 365 - (151 + 31)

= 365 - 182

= 183 days

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The truck travelled 0.42 miles per minute

The given parameters are:

Distance = 75 miles

Time = 3 hours

Convert time to minutes

Time = 3 * 60 minutes

Time = 180 minutes

The speed is calculated as:

Speed = Distance/Time

This gives

Speed = 75 miles/180 minutes

Evaluate

Speed = 0.42 miles per minutes

Hence, the truck travelled 0.42 miles per minute

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