Yui is buying beverages for her friends. She buys a total of 6 bottles of water and sports drinks. Bottles of water cost $1.50 each, and sports drinks cost $2.50 each. She spends a total of $10. Write a system of equations to represent the information, and use substitution to determine how many of each type of drink Yui buys.

A reflection over the x-axis changes the signs of the y-coordinates of the points, and a translation left 2 and down 1 changes the position of the figure, but it does not change the orientation of the figure.

A 90 degree counterclockwise rotation about the origin followed by a translation up 3 produces A’B’C’ from ABC. A 90 degree counterclockwise rotation about the origin changes the coordinates of the points, but it does not change the relative positions of the points. The translation then moves the entire figure up 3 units along the y-axis. A reflection over the x-axis changes the signs of the y-coordinates of the points, and a translation left 2 and down 1 changes the position of the figure, but it does not change the orientation of the figure.

A translation left 5 and down 2 followed by a reflection over the x-axis changes the position and orientation of the figure, but it does not produce the same result as a 90 degree counterclockwise rotation about the origin followed by a translation up 3.

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The product of the expression (-4) x (-4) x (-4) x y x y is -64y²

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given that, an expression, (-4) x (-4) x (-4) x y x y

We need to find its product,

(-4) x (-4) x (-4) x y x y

= -4³ × y²

= -64 × y²

= -64y²

Hence, the product of the expression (-4) x (-4) x (-4) x y x y is -64y²

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Answer:

Step-by-step explanation:

The equation of the line in point-slope form can be written as:

y - 0 = -1/4 (x - 1)

where (1, 0) is the point and -1/4 is the slope of the line.

Answer:

48

Step-by-step explanation:

48+96 =144

x * (1+2) = 3x = 144

so x = 48

We are 90% confident that the true proportion of times the die would land on the number 1 is between 0.438 and 0.602. Since this includes 0.5, the die appears to be fair.

The correct option is C.

The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.

Given:

While playing a game of chance,

Tarik rolled a regular six-sided die 100 times and noticed that it landed on the number 1 exactly 52 times.

The probability P is = 52/100 = 0.52.

The lower limit = P - z√(P(1 - P)/n

The lower limit = 0.52 - 1.645√(0.52 x 0.48)/100

The lower limit ≈ 0.438.

The upper limit = P + z√(P(1 - P)/n

The upper limit = 0.52 + 1.645√(0.52 x 0.48)/100

The upper limit ≈ 0.602.

Therefore, the die would land on the number 1 is between 0.438 and 0.602.

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(b) Yes, the experiment has a control group.

(c) The treatments can be randomly assigned to the experimental units by randomly selecting 20 containers and assigning each of the four treatments to 5 containers.

a) Treatments: Four different concentrations of fungus mixtures (0 ml/L, 1.25 ml/L, 2.5 ml/L, and 3.75 ml/L).

Experimental units: 20 individual containers with a group of insects.

Response variable: Number of insects that are still alive in each container one week after spraying.

(b) A control group is used to compare the results of the treatment group to a group that is not exposed to the treatment.

In this experiment, the control group can be the group of insects that are not exposed to any of the fungus mixtures.

c) The treatments can be randomly assigned to the experimental units by randomly selecting 20 containers and assigning each of the four treatments to 5 containers.

This way, each treatment has the same number of units and the assignment of treatments to units is random, which reduces the risk of bias in the experiment.

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Answer:

The slope is 5/2 and the y-intercept is -9.

Step-by-step explanation:

You do not have to graph anything for this problem, as the slope and y-intercept are already in the problem.

The least integer k such that f(n) is O(nk) for each of the following functions is k = 2.

log (n!) = ln(n!)

First we know ,

[tex]\lim_{n \to \infty} \frac{ln(n!)}{n^{k} } = L[/tex]

where L is a limited number.

then ,

[tex]\lim_{n \to \infty} \frac{ln(n!)}{n^{k} } = L \\\\\lim_{n \to \infty} \frac{ln(n+1)!-ln(n!)}{(n+1)^{k}- n^{k} } = L[/tex]     Stolz's Formula

By solving the upper limit we get k =2

It can make  

[tex]\lim_{n \to \infty} \frac{1}{k} \frac{ln(n+1)}{n^{(k-1)} } _[/tex]

[tex]\lim_{n \to \infty} \frac{1}{2} \frac{ln(n+1)}{n^{} } = 0[/tex]

The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain.

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7/3 t^(3/2) + C This equation represents the volume of water in the tank as a function of time t.

The equation r(t) = 7t √ represents the rate at which water is flowing into the tank, measured in cubic feet per hour, at time t after 9:00am. The expression 7t √ means that the rate of flow increases over time, starting at 0 cubic feet per hour at t = 0 and increasing as t increases.

To find the volume of water in the tank at a specific time t after 9:00am, we can integrate the rate of flow over the time interval from 9:00am to t. The volume of water in the tank at time t can be expressed as:

V(t) = ∫ r(t) dt from 9:00am to t

= ∫ 7t √ dt from 0 to t

= 7/3 t^(3/2) + C

where C is an arbitrary constant of integration. This equation represents the volume of water in the tank as a function of time t.

Therefore, 7/3 t^(3/2) + C This equation represents the volume of water in the tank as a function of time t.

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a. Fraction of earnings that Mariano put into each piggy bank  is 1/12

b. Mariano earns $28.8

Mariano divides his earnings into a saving account and 3 piggy banks.  

First,  we have to know the fraction that we divide in the 3 piggy banks.

Piggy banks =Total earning-Saving account

Saving account 3/4,  

Total earnings is 1

to rest both terms we have to get the same denominator, so we can say that the total earning is 4/4

Piggy banks =4/4-3/4=( 4-3)/4=1/4

Piggy banks =1/4

Each piggy bank will be 1/3 of that 1/4

1/3 x 1/4=

For fraction multiplication, multiply the numerators and then multiply the denominators to get

1×1/3×4=1/12

This fraction cannot be reduced.

b. Mariano adds $2.40

1/12 is 2.40

We use cross-multiplication

a/b=c/d  replacing   (1/12)/2.40 = 1/ ?

So,  the total earning (?) is 1 x 2.40/ (1/12)

= 2.40 x 12=$28.8

Complete question:

Mariano delivers newspapers. He always puts 3/4 of his weekly earnings in his savings account and then divides the rest equally into 3 piggy banks for spending at the snack shop, the arcade, and the subway.

a. What fraction of his earnings does Mariano put into each piggy bank?

b. If Mariano adds $2.40 to each piggy bank every week, how much does Mariano earn per week delivering papers?

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Mariano always puts 3/4 of his weekly earnings in his savings account and then 1/4 part  divides into 3 piggy banks and in each it has 1/12 .

Let the total income of Mariano who delivers newspaper be x.

He puts 3/4(x) of his total income of his weekly earnings in his savings account.

The remaining income be x/4 and it is divided into 3 piggy banks.

so the income divides into each piggy bank will be 1/3(x/4) = x/12

so, therefore the amount that Mariano puts in each piggy bank is 1/12 part of his weekly income.

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Total mortgage brokerage fees is $1,596.75. Thus, option c is correct.

These factors include the total amount you're borrowing from a bank, the interest rate for the loan, and the amount of time you have to pay back your mortgage in full. For your mortgage calc, you'll use the following equation: M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1].

Calculate H = P*J, this is your current monthly interest.

Calculate C = M - H, this is your monthly payment minus your monthly interest, so it is the amount of principal you pay for the month.

Calculate Q = P - C, this is the new balance of your principal of your loan.

P = the payment.

L = the loan value.

c = the period interest rate, which consits of dividing the APR as a decimal by the frequency of payments. ...

n = the total number of payments in the life of the loan (for monthly loan payments this is the loan term in years times twelve)

With given data:

123,500 x 1.05% =$1,296.75 percentage of the fee.

Total mortgage brokerage fees

$1,296.75 + $300 =$1,596.75

Thus, Total mortgage brokerage fees is $1,596.75. Thus, option c is correct.

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Answer:

$400

Step-by-step explanation:

25% = 0.25

320 times 0.25 = $80

$320 + $80 = $400

So, the Johnsons set aside $400 in their budget for food for the party.

The Rational Root Theorem states that for a polynomial equation with integer coefficients to have a rational solution, that solution must be represented by the a factor of the constant (denoted by the variable p) divided by a factor of the leading coefficient (denoted by the variable q).

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The lengths 6, 8 and 15 cannot represent the sides of the triangle. The solution has been obtained by using the triangle inequality theorem.

What is the triangle inequality theorem?

The triangle inequality theorem outlines the relationships between a triangle's three sides. According to this theorem, the lengths of any triangle's two shorter sides add up to be longer than the triangle's third side. In other terms, this theorem states that the shortest path between any two places is always a straight line.

We are given the lengths to be 6, 8 and 15.

Using the triangle inequality theorem,

⇒ 6 + 15 > 8

⇒ 21 > 8

Also,

⇒ 8 + 15 > 6

⇒ 23 > 8

Also,

⇒ 6 + 8 > 15

But,

⇒ 14 < 15

Hence, the lengths 6, 8 and 15 cannot represent the sides of the triangle.

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The meaning of the slope and of the intercept of the linear function are given as follows:

The slope is negative -3/2, and the y-intercept is 9. The candle starts at a height of 9 inches and decreases 3/2 of an inch every hour.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The two points for the function in this problem are given as follows:

(0,9) and (2,6).

When x = 0, y = 9, hence the intercept b is given as follows:

b = 9.

Meaning that the initial value of the problem is of 9.

The slope is given as the change in y divided by the change in x, hence:

m = (6 - 9)/(2 - 0)

m = -3/2.

Meaning that the rate of change is a decrease of 3/2 units for each unit of the input.

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If Six Republicans and six Democrats orally cast their vote in the U.S. Senate , if they are alternate Republican, Democrat, Republican, Democrat, and so on, and if a Republican must always be the first to vote then the number of ways in which they can vote is 518400 ways .

the number of Republicans for voting is = 6 ;

the number of Democrats for voting is = 6 ;

so , total number of voters is = 12 ,

they have to vote alternately starting with a Republicans .

the first republican has to choose from = ⁶C₁ = 6 ;

the second republicans has to choose from the remaining 5 republicans , = ⁵C₁ = 5 ;

Similarly following the pattern ,

we get ;

Total chances of required way of casting votes ;

= 6×6×5×5×4×4×3×3×2×2×1×1

= (1×2×3×4×5×6)²

= (6!)² = (720)² = 518400 ways .

Therefore , the number of ways of voting is 518400 ways .

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[tex]$\int_{-2}^{4} f(x)dx$[/tex] with the substitution [tex]$u = x^2$[/tex] . The new limits of integration are 0 and 8.

The substitution [tex]$u = x^2$[/tex] implies that [tex]$du = 2x dx$[/tex], so when [tex]x = -2$, $u = (-2)^2 = 4$[/tex]. Similarly, when [tex]x = 4$, $u = 4^2 = 16$[/tex]. Thus, the new limits of integration are 0 and 8.

To determine the new limits of integration, we must first find the values of u for the original limits of integration. Since we have [tex]$u = x^2$[/tex], when x = -2, we have [tex]$u = (-2)^2 = 4$[/tex]. Similarly, when x = 4, we have [tex]u = 4^2 = 16$.[/tex]Therefore, the new limits of integration are 0 and 8.

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When u, v are nonzero vectors, then span{u, v} contains the line through u and the origin, as well as the line through v and the origin, this statement is false.

The span of two nonzero vectors, u and v, is the set of all linear combinations of u and v. This can be a line, a plane, or even the entire space, depending on the vectors u and v. In general, the span of two nonzero vectors does not contain the line through each vector and the origin, unless the two vectors are collinear (i.e. they lie on the same line).

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The time it take to paint this cone if it can be painted at the same rate is 4.21 minutes.

The region that includes the base(s) and the curved portion is referred to as the total surface area. It is the overall area that the object's surface occupies. The total area of a shape with a curved base and surface is equal to the sum of the two areas.

Given:

Base area = 49π in²

h= 8 inches

So, area of a circle, A = πr^2

r = √(A/π).

r = √(49π/π)

r = 7 in.

Now, they doubled cone has a base area

= 2 x 49 in²

= 98 π in²

Then, r = √(98π/π)

r = 7√2 inch

Thus, the time taken

= TSA (R= 7) / TSA (r= 7√2) x2.5

= πR(l+ R) / πr(l+r)

= 14(4√2+7)π/105π x 2.5

= 4.21 min

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The expression that correctly represents the cost of a bag of dog food to the customer in terms of (m), the original market price is 1.5m

As per the given data Pam’s Pet Supply Palooza buys bags of dog food directly from the manufacturer.

Market Price = m

Got 50% discount off the original market price.

Discount = 50%

Pam then sells each bag of dog food at a price that is 3 times the amount that she paid for it.

Selling Price =3 × (Amount she paid)

If she gets a discount of 50 %, then she pays 50 % (100 - 50% ).

So, the amount she paid is:

Amount = 50 % × Market Price

Amount = [tex]$\frac{50}{100}[/tex] × m

Amount = 0.5 × m

Amount = 0.5 × m

She sells at three times that amount.

So, the selling price is:

Selling Price = 3 × 0.5 m

Selling Price = 1.5 m

Therefore the expression is 1.5 m.

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Answer:

a) $2125

b) $2000

Step-by-step explanation:

In this problem, we are asked to solve for the manufacturing price of different printers if the printer company sells their printers at a price that makes them 25% profit, assuming there are no extra expenses.

We can solve this type of problem by manipulating ratios, like for example:

manufacturing price : sale price

           100                  :       125

This ratio represents the the sale price being 25% more than the manufacturing price.

a) We can equate the above ratio to the ratio of the manufacturing price (in this problem, $1700) to the sale price of the printer (represented by x).

100 : 125 = 1700 : x

This can be solved for x when the ratios are represented as fractions.

[tex]\dfrac{100}{125} = \dfrac{1700}{x}[/tex]

↓ simplify the fraction on the left side

[tex]\dfrac{4}{5} = \dfrac{1700}{x}[/tex]

↓ cross multiply

[tex]4x = 1700 \cdot 5[/tex]

↓ divide both sides by 4

[tex]x=\$ \, 2125[/tex]

So, the price that the customer would pay for a printer that the company bought for $1700 is $2125.

b) We can solve in the same way that we did for section a.

However, this time, the variable (y) represents the manufacturing price, NOT the sale price.

100 : 125 = y : 2500

↓ rewrite with fractions

[tex]\dfrac{100}{125} = \dfrac{y}{2500}[/tex]

↓ simplify the fraction on the left side

[tex]\dfrac{4}{5} = \dfrac{y}{2500}[/tex]

↓ cross multiply

[tex]5y = 2500 \cdot 4[/tex]

↓ divide both sides by 5

[tex]y = \$ \, 2000[/tex]

So, the price that the company would pay for a printer that a customer buys for $2500 is $2000.

The container that has the following dimensions 120cm×300cm×430cm can hold 15480 liters of liquid

It is the space occupied by a body, it is calculated by multiplying its dimensions, for example: length, height and width.

Calculating the volume of the container we get the liter of liquid it can hold in cubic centimeters :

v = h*l*w

v = 120cm×300cm×430cm

v = 15480000 cubic centimeters

Converting the volume from cubic centimeters to liter we have:

1 liter is equal to 1000 cubic centimeters

x = 15480000 cubic centimeters * (1 liter / 1000 cubic centimeters)

x = 15480 liters

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The x and y-intercept for -4x+y = 8 is  (-2,0) and (0, 8)

What is the intercept?

The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively. The slope intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given is also the y-intercept (0, b).

Here, we have

Given: -4x+y = 8

Let's start with the interception point with the x-axis. Here we know that y = 0, so we can put that in our original expression:

-4x = 8

x = -2

The function intercepts the x-axis at (-2, 0)

Let's continue with the y-axis. Here we know that  x = 0, so let's put that into our expression/function:

y = 8

This gives us an interception point with a y-axis at (0, 8)

Hence, the x and y-intercept for -4x+y = 8 is (-2,0) and (0, 8)

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Answer: 40.75

Step-by-step explanation:

-2.25 is larger when it compares to -3, because when you order negative numbers, the larger the number after the negative sign, the smaller the number actually is. This means -2.25 > -3

What is negative numbers?

On a number line, numbers always move from right to left and grow (become "more positive") in that direction. The numbers to the right are bigger than the numbers to the left, while the numbers to the left are smaller. Numbers with a minus sign before them are considered negative numbers. They could be fractions, decimals, or integers. Negative numbers include, for instance, -4, -15, -4/5, and -0.5. A negative number in mathematics represents the reverse. A negative number is one that is less than zero in the real number system. Negative numbers are frequently used to indicate how great a loss or a shortage is.

-2.5>-3 because the bigger a negative number is like -15,-18, etc the smaller it’s value actually gets so -2.5 is greater because it is closer to 0 on a number line.

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Answer:

i think its 2 but i am not sure

Since Fathi has $1.10 in his printing account, he will have -$59342.28 after printing the 474747-page PDF document.

Let's calculate how much Fathi will spend on printing the 474747-page PDF document.

Since Fathi is printing 2 pages on each side of a sheet, he uses 1/2 sheet of paper per 2 pages. And since each sheet of paper reduces his printing account balance by $0.25, he will spend $0.25 per 2 pages.

So, the cost per page is $0.25 / 2 = $0.125.

Now, we can calculate the total cost of printing the 474747 pages by multiplying the cost per page by the number of pages:

$0.125 * 474747 = $59343.38

Since Fathi has $1.10 in his printing account, he will have $1.10 - $59343.38 = -$59342.28 after printing the 474747-page PDF document.

So, Fathi will not have enough funds in his printing account to print the document and will have to add more money to his account or find another way to print the document.

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Since Fathi has $1.10 in his printing account, he will have -$59342.28 after printing the 474747-page PDF document.

Let's calculate how much Fathi will spend on printing the 474747-page PDF document.

Since Fathi is printing 2 pages on each side of a sheet, he uses 1/2 sheet of paper per 2 pages. And since each sheet of paper reduces his printing account balance by $0.25, he will spend $0.25 per 2 pages.

So, the cost per page is $0.25 / 2 = $0.125.

Now, we can calculate the total cost of printing the 474747 pages by multiplying the cost per page by the number of pages:

$0.125 * 474747 = $59343.38

Since Fathi has $1.10 in his printing account, he will have $1.10 - $59343.38 = -$59342.28 after printing the 474747-page PDF document.

So, Fathi will not have enough funds in his printing account to print the document and will have to add more money to his account or find another way to print the document.

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It is found that 22 miles in 20 minutes is LESS

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We have to compare the two rates:

=> 22 miles in 20 minutes

=> 38 miles in 30 minutes

Let's simplify each rate by finding the speed, which is distance divided by time.

That is:

Speed = distance/time

For the first one:

s = 22/20 = 1.1 milesl/min

For the second one:

s = 38/30 = 1.27 milesl/min

Since 1.1 is less than 1.27, so, 22 miles in 20 minutes is less than 38 miles in 30 minutes.

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The complete question is;

Is 22 miles in 20 minutes greater than, equal to or less than 38 miles in 30 minutes?

Answer:

Step-by-step explanation:

The given exponential function will grow at 6.1%

Given,

y =

To find,

identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.

Solution,

We have,

y =

The equation represents exponential growth because the growth factor is greater than 1.

The general form equation is:

y(x)= a(1-r)^x such that r is the growth percent.

==> 1+r = 1.061

==> r = 0.061 = 6.1%

Answer:

1320

MDAS Method

Answer:

Your answer is 1320

Step-by-step explanation:

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