Consider the following points. M(3,4) and T(-2,3) MT undergoes the translation (x,y) - (x + h, y + k), such that M'(7,1) and T'(2,0). Complete the following algebraic description. (x,y) → (x+4y+​

Answer:

a) \(a = 2\) and \(b = -4\), b) \(c = -10\), c) \(f(-2) = -\frac{5}{3}\), d) \(y = -\frac{5}{2}\).

Step-by-step explanation:

a) After we read the statement carefully, we find that rational-polyomic function has the following characteristics:

1) A root of the polynomial at numerator is -2. (Removable discontinuity)

2) Roots of the polynomial at denominator are 1 and -2, respectively. (Vertical asymptote and removable discontinuity.

We analyze each polynomial by factorization and direct comparison to determine the values of \(a\), \(b\) and \(c\).

Denominator

i) \((x+2)\cdot (x-1) = 0\) Given

ii) \(x^{2} + x-2 = 0\) Factorization

iii) \(2\cdot x^{2}+2\cdot x -4 = 0\) Compatibility with multiplication/Cancellative Property/Result

After a quick comparison, we conclude that \(a = 2\) and \(b = -4\)

b) The numerator is analyzed by applying the same approached of the previous item:

Numerator

i) \(c\cdot x - 5\cdot x^{2} = 0\) Given

ii) \(x \cdot (c-5\cdot x) = 0\) Distributive Property

iii) \((-5\cdot x)\cdot \left(x-\frac{c}{5}\right)=0\) Distributive and Associative Properties/\((-a)\cdot b = -a\cdot b\)/Result

As we know, this polynomial has \(x = -2\) as one of its roots and therefore, the following identity must be met:

i) \(\left(x -\frac{c}{5}\right) = (x+2)\) Given

ii) \(\frac{c}{5} = -2\) Compatibility with addition/Modulative property/Existence of additive inverse.

iii) \(c = -10\) Definition of division/Existence of multiplicative inverse/Compatibility with multiplication/Modulative property/Result

The value of \(c\) is -10.

c) We can rewrite the rational function as:

\(f(x) = \frac{(-5\cdot x)\cdot \left(x+2 \right)}{2\cdot (x+2)\cdot (x-1)}\)

After eliminating the removable discontinuity, the function becomes:

\(f(x) = -\frac{5}{2}\cdot \left(\frac{x}{x-1}\right)\)

At \(x = -2\), we find that \(f(-2)\) is:

\(f(-2) = -\frac{5}{2}\cdot \left[\frac{(-2)}{(-2)-1} \right]\)

\(f(-2) = -\frac{5}{3}\)

d) The value of the horizontal asympote is equal to the limit of the rational function tending toward \(\pm \infty\). That is:

\(y = \lim_{x \to \pm\infty} \frac{-10\cdot x-5\cdot x^{2}}{2\cdot x^{2}+2\cdot x -4}\) Given

\(y = \lim_{x \to \infty} \left[\left(\frac{-10\cdot x-5\cdot x^{2}}{2\cdot x^{2}+2\cdot x-4}\right)\cdot 1\right]\) Modulative Property

\(y = \lim_{x \to \infty} \left[\left(\frac{-10\cdot x-5\cdot x^{2}}{2\cdot x^{2}+2\cdot x-4}\right)\cdot \left(\frac{x^{2}}{x^{2}} \right)\right]\) Existence of Multiplicative Inverse/Definition of Division

\(y = \lim_{x \to \pm \infty} \left(\frac{\frac{-10\cdot x-5\cdot x^{2}}{x^{2}} }{\frac{2\cdot x^{2}+2\cdot x -4}{x^{2}} } \right)\)   \(\frac{\frac{x}{y} }{\frac{w}{z} } = \frac{x\cdot z}{y\cdot w}\)

\(y = \lim_{x \to \pm \infty} \left(\frac{-\frac{10}{x}-5 }{2+\frac{2}{x}-\frac{4}{x^{2}} } \right)\)   \(\frac{x}{y} + \frac{z}{y} = \frac{x+z}{y}\)/\(x^{m}\cdot x^{n} = x^{m+n}\)

\(y = -\frac{5}{2}\) Limit properties/\(\lim_{x \to \pm \infty} \frac{1}{x^{n}} = 0\), for \(n \geq 1\)

The horizontal asymptote to the graph of f is \(y = -\frac{5}{2}\).

Using asymptote concepts, it is found that:

a) Building a quadratic equation with leading coefficient 2 and roots 1 and -2, it is found that a = 2, b = -4.

b) c = -10, since the discontinuity at x = -2 is removable, the numerator is 0 when x = -2.

c) Simplifying the function, it is found that at \(x = -2, f(x) = -\frac{5}{3}\).

d) The equation for the horizontal asymptote to the graph of f is \(y = -\frac{5}{2}\)

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

Item a:

\(2(x - 1)(x - (-2)) = 2(x - 1)(x + 2) = 2(x^2 + x - 2) = 2x^2 + 2x - 4\)

\(2x^2 + ax + b = 2x^2 - 2x - 4\)

Thus a = 2, b = -4.

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

Item b:

\(-2c - 5(-2)^2 = 0\)

\(-2c - 20 = 0\)

\(2c = -20\)

\(c = -\frac{20}{2}\)

\(c = -10\)

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

Item c:

With the coefficients, the function is:

\(f(x) = \frac{-10x - 5x^2}{2x^2 + 2x - 4} = \frac{-5x(x + 2)}{2(x - 1)(x + 2)} = -\frac{5x}{2(x - 1)}\)

At x = -2:

\(-\frac{5(-2)}{2(-2 - 1)} = -\frac{-10}{-6} = -(\frac{5}{3}) = -\frac{5}{3}\)

Thus, simplifying the function, it is found that at \(x = -2, f(x) = -\frac{5}{3}\)

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

Item d:

The horizontal asymptote of a function is:

\(y = \lim_{x \rightarrow \infty} f(x)\)

Thus:

\(y = \lim_{x \rightarrow \infty} \frac{-10x - 5x^2}{2x^2 + 2x - 4} = \lim_{x \rightarrow \infty} \frac{-5x^2}{2x^2} = \lim_{x \rightarrow \infty} -\frac{5}{2} = -\frac{5}{2}\)

The equation for the horizontal asymptote to the graph of f is \(y = -\frac{5}{2}\)

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The number of hours it will take both the surveyor and apprentice to complete the same job is 15/56 hours.

If the two work together;

Time taken for both to complete the task = Surveyors rate of work + Apprentice rate of work

= 1/8 + 1/7

= (7+8) / 56

= 15/56 hours

Therefore, the number of hours it will take both the surveyor and apprentice to complete the same job is 15/56 hours.

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The inverse of (- 2 . 3 ) is (1 / - 2.3 ).

In mathematics, the inverse of a number refers to the concept of taking its reciprocal; for instance (2 . w ) results in its reciprocal as ( 1/ 2. w ). When a number is multiplied by its inverse the result yields 1, meaning that the product of the number and its inverse, i.e. reciprocal always equals 1.

As per the given number which is (-2.3) and its inverse is ( 1 / -2.3 ), when these two numbers are multiplied together they result in 1. Such as:

(-2.3) x ( 1 / -2.3 ) = 1

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Answer:

u≤25

Step-by-step explanation:

63 ≥ 3u-12

-3u    -3u

-3u+63 ≥ -12

 -63        -63

-3u ≥ -75

/-3    /-3

u≤25

Answer:

f =38

Step-by-step explanation:

f-3/4=5/6

f-3×6=5×4

f-18 =20

f =20+18

f =38

The total cost for 10 hours of work would be 25 + 50(10) = 525.

Cost is the monitorial associated with the purchase of production of food or service if can include the prices of material of which is over it and other expenses that are related to the production of the code of service cost is a major fraction of when deciding whether to purchase a product something as it is and indicator of the value of the product of sound service.
The marginal cost of producing 5 items can be calculated using the equation C(x)=1300+4x/10. The marginal cost is the cost associated with producing one additional item. To calculate the marginal cost, we can plug in x=5 into the equation.

The equation in slope-intercept form for cost, c, after h hours of service is c = 25 + 50h.

The total cost for 8 hours of work would be 25 + 50(8) = 425.

The total cost for 10 hours of work would be 25 + 50(10) = 525.

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The Hadamard gate can be expressed as H = e^(iα)AXBXC, where α is a phase factor and A, B, and C are specific matrices that satisfy ABC = I, the identity matrix. Additionally, the Hadamard gate can also be represented as the product of rotations about the x and y axes.

a) The Hadamard gate, denoted as H, can be expressed as H = e^(iα)AXBXC, where e^(iα) is a phase factor and A, B, and C are matrices. These matrices are chosen such that their product, ABC, equals the identity matrix, I. By setting α to an appropriate value, we can determine the phase factor required for the Hadamard gate.

b) Another way to represent the Hadamard gate is through rotations about the x and y axes. The Hadamard gate can be expressed as H = R_y(π/4)R_x(π/2), where R_x(π/2) represents a rotation of π/2 radians about the x axis, and R_y(π/4) represents a rotation of π/4 radians about the y axis. This representation highlights the geometric interpretation of the Hadamard gate as a combination of rotations.

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The explicit formula for the nth term of the sequence 14,16,18,... is aₙ = 2n + 12.

What is an explicit formula?

The explicit equations for L-functions are the relationships that Riemann introduced for the Riemann zeta function between sums over an L-complex function's number zeroes and sums over prime powers.

Here, we have

Given:  the sequence 14,16,18,….

First term a₁ = 14

Common difference d = 16 - 14 = 2

Now, plug the values into the above formula and simplify.

aₙ = a₁ + d( n - 1 )

aₙ = 14 + 2( n - 1 )

aₙ = 14 + 2n - 2

aₙ = 14 - 2 + 2n

aₙ = 2n + 12

Hence,  the explicit formula is aₙ = 2n + 12.

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Answer:

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Identity:

An identity is an equality which is true for all values of a variable in the equality.

(a + b)³ = a³+ b³+ 3ab(a + b)

In an identity the right hand side expression is called expanded form of the left hand side expression.

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

Solution:

(i) (2x + 1)³

Using identity

(a + b)³ = a³+ b³+ 3ab(a + b)

(2x + 1)³

= (2x)³ + 1³ + (3×2x×1)(2x + 1)

= 8x³+ 1 + 6x(2x + 1)

= 8x³ + 1 + 12x² + 6x

(ii) (2a – 3b)³

Using identity,

(a – b)³ = a³–b³ – 3ab(a – b)

(2a – 3b)³ = (2a)³– (3b)³ – (3×2a×3b)(2a – 3b)

=8a³–27b³–18ab(2a –3b)

= 8a³–27b³–36a²b + 54ab²

(iii) [3x/2  + 1]³

Using identity,

(a + b)³ = a³+ b³+ 3ab(a + b)

[3x/2 +1]³

=(3x/2)³+1³+ (3×(3x/2)×1)(3x/2+ 1)

=27x³/8+1+9/2x×(3x/2+1)

= 27x³/8 + 1 + 27/4 x² + 9/2x

= (27/8)x³ + (27/4) x² + 9/2 x + 1

(iv) [x–2/3 y]³

Using identity,

(a - b)³=a³-b³-3ab(a-b)

(X+ 2/3y)³

= (x)³–(2/3 y)³– (3×x×2/3 y)(x – 2/3 y)

= x³– 8y³/27–2xy(x – 2/3 y)

= x³– (8/27)y³–2x²y+ 4/3xy²

=========================================================

Hope this will help you....

Step-by-step explanation:

If the a has 15 boys and 20 girls, then the boy to girls ratio in simplest form is 3 : 4

Number of boys in the class = 15 boys

Number of girls in the class = 20 girls

The ratio can be defined as the a number that can be used to express one quantity as a fraction of the other ones. That means we are comparing them by dividing those numbers

Here the ratio will be

Number of boys in the class : Number of girls in the class

Substitute the values in the ratio

= 15 : 20

Divide both numbers by 5

= (15/5) : (20/5)

= 3 : 4

Hence, if the a has 15 boys and 20 girls, then the boy to girls ratio in simplest form is 3 : 4

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The two numbers required to solve the following problem are, 13.3 and 6.7

What is Derivative?

The derivative of a function of a real variable in mathematics describes the sensitivity of the function value to a change in its argument. Calculus relies heavily on derivatives.

Solution:

Let the ture positive numbers be x,(x,y>0)

x + y = 20 -------- Given

We need to maximise \(xy^{2}\)

x = 20 - y

f(y) = (20 - y)*\(y^{2}\)

f(y) = 20\(y^{2}\) - \(y^{3}\)

f'(y) = 0

On differentiating:

f'(y) = 40y - 3\(y^{2}\)

0 = 40 - 3y

y = 13.3

x = 6.7

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In order to calculate the time it will take for Andrew to settle the loan, we can use the formula for compound interest. So, it will take Andrew approximately 5.22 years to settle the loan.

The formula is given as A = P(1 + r/n)^(nt), Where: A = the final amount, P = the principal (initial amount borrowed), R = the annual interest rate, N = the number of times the interest is compounded in a year, T = the time in years.

We know that Andrew borrowed R200 000 from a bank at an annual interest rate of 5.25% compounded quarterly and that he will make repayments of R6 000 at the end of every 3 months.

Since the first repayment will be made 3 months from now, we can consider that the initial loan repayment is made at time t = 0. This means that we need to calculate the value of t when the total amount repaid is equal to the initial amount borrowed.

Using the formula for compound interest: A = P(1 + r/n)^(nt), We can calculate the quarterly interest rate:r = (5.25/100)/4 = 0.013125We also know that the quarterly repayment amount is R6 000, so the amount borrowed minus the first repayment is the present value of the loan: P = R200 000 - R6 000 = R194 000

We can now substitute these values into the formula and solve for t: R194 000(1 + 0.013125/4)^(4t) = R200 000(1 + 0.013125/4)^(4t-1) + R6 000(1 + 0.013125/4)^(4t-2) + R6 000(1 + 0.013125/4)^(4t-3) + R6 000(1 + 0.013125/4)^(4t)

Rearranging the terms gives us: R194 000(1 + 0.013125/4)^(4t) - R6 000(1 + 0.013125/4)^(4t-1) - R6 000(1 + 0.013125/4)^(4t-2) - R6 000(1 + 0.013125/4)^(4t-3) - R200 000(1 + 0.013125/4)^(4t) = 0

Using trial and error, we can solve this equation to find that t = 5.22 years (rounded to 2 decimal places). Therefore, it will take Andrew approximately 5.22 years to settle the loan.

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Answer:

0

Step-by-step explanation:

Answer:

the answer is undefined.

Step-by-step explanation:

-9-3

5-5

-12⇒

0⇔          its undefined.don´t forget to brainllest.

A statistical technique that would allow a researcher to cluster such traits as being talkative, social, and adventurous with extroversion is called factor analysis.

Statistical techniques are methods and procedures used in the collection, analysis, interpretation, and presentation of data. These techniques involve the use of mathematical and statistical models to draw meaningful insights and conclusions from data.

Some common statistical techniques include:

Descriptive statistics: These techniques are used to summarize and describe the key features of a dataset, such as central tendency, variability, and distribution.

Inferential statistics: These techniques are used to make inferences about a larger population based on a sample of data. This involves using probability theory to estimate population parameters and test hypotheses.

Regression analysis: This technique is used to model the relationship between one or more independent variables and a dependent variable.

Hypothesis testing: This technique is used to test the validity of a hypothesis or claim about a population using sample data.

Time series analysis: This technique is used to analyze data that varies over time, such as stock prices or weather patterns.

Cluster analysis: This technique is used to group similar observations together based on their characteristics.

Data mining: This technique involves the use of automated methods to discover patterns and relationships in large datasets.

Statistical techniques are widely used in many fields, including business, economics, social sciences, medicine, and engineering. They are used to make informed decisions, identify trends and patterns, and to understand complex systems.

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Angle 1 has a measure of greater than 97° and no more than 115°. (that means less than or equal to)

An angle is formed when two straight lines or rays meet at a single terminal. The place where two points converge is known as an angle's vertex. The Latin term "angulus," which means "corner," is whence the word "angle" gets its name." An angle is a shape in planar geometry made up of two rays or lines that have a common termination. The English word "angle" derives from the Latin word "angulus," which means "corner." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.

This means that:

< 1 ? 97

< 1 ≤ 115

Angle 1 in the diagram is equivalent to (9x + 7). Because they are different internal angles, this is the case.

Hence, the following follows:

9x+7 ? 97

And

9x+7 ≤ 115

Solve for x:

9x? 97-7

9x? 90

Divide through by 9

x? 10

And

9x ≤ 115-7

9x ≤ 108

Divide through by 9

x ≤ 12

10i ≤ 12

As a result, the following is the number line graph representing the range of potential values of x:

The number line is that.

0   2   4    6    8    10    12  

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Answer:

A: first choice

x^4

Step-by-step explanation:

When you divide two powers with the same base, you subtract the exponents, not divide.

The step x^8/x^4 is correct.

The next step should be x^(8 - 4), not x^8/4.

The correct simplification is x^4.

Answer:

A: first choice

x^4

Answer:

Option C: 4

Hope this helps!

Answer:

Step-by-step explanation:

This problem is about our wet clothe, when we put it under the Sun to dry.

Notice that the clothe is wet at the beginning, but after a certain time, it gets dry. This phenomenon is beacuse the change of the state of the water inside the clothe.

You see, at the beginning, the water is in liquid state making the wet effect, then that water transforms into vapor, makign the dry effect.

Therefore, the answer is "liquid water to vapor water", that's the change.

The car will cost $ 800 after a depreciation time of approximately 6 years.

Herein we are informed about the case of a car bought in 2011 at a cost of $ 36,000 and that depreciates linearly every year. Then, the depreciation function is described below:

c(t) = c' + m · t

Where:

If we know that c(0) = 36,000, c(4) = 12,000 and c(t) = 800, then the depreciation rate is:

m = (12,000 - 36,000) / (4 - 0)

m = - 24,000 / 4

m = - 6,000

800 = 36,000 - 6,000 · t

6,000 · t = 35,200

t = 35,200 / 6,000

t = 5.867

The expected depreciation time is approximately 6 years.

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The solution to the given differential equation as required is; y = √(x² + 4).

As evident in the task content;

dy / dx = x / y, y(0) = -2

Therefore, we have that;

dy (y) = dx (x)

By integration of both sides indefinitely;

y² / 2 = x²/2 + C

y² = x² + 2c

y = √(x² + 2c)

Hence, using the initial conditions;

-2 = √(0² + 2c)

-2 = √2c

2c = 4

c = 2.

Hence, the required solution of the differential equation as given is; y = √(x² + 4) since c = 2.

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Given the following function:

Where x is the time in years, models a declining lemming population.

We will find the number of lemmings after 5 years

So, we will substitute x = 5

Rounding to the nearest whole number

so, the number of lemmings after 5 years = 5840

Answer:

the specific answer is 5,840

Answer:

A) inside the circle

Step-by-step explanation:

equation of the circle is:

\((x-a)^{2} + (y-b)^{2} = r^{2}\)

where (a,b) is center of the circle and r is radius so

\(x^{2} + y^{2} = r^{2}\) now plug in given point to find the radius

\((6)^{2} + (-4)^{2} = r^{2}\)

36 +16 = 52 so

r = \(\sqrt{52}\)  ≈ 7.2 or  \(r^{2} =52\)

when you plug point (√2 , -7) into equation of the circle

(√2)^2 + (-7)^2 = 2 +49 =51

51 is less than 52 so this is inside of the circle

Answer:

y = -5

...

.............

a) To obtain the potential pressure drop in the wellbore, we can use the hydrostatic pressure equation.

The potential pressure drop is equal to the pressure gradient multiplied by the length of the wellbore. The pressure gradient can be calculated using the equation: Pressure gradient = (density of oil × acceleration due to gravity) × sin(θ), where θ is the deviation angle of the wellbore from horizontal flow. In this case, the pressure gradient would be (48 lbm/ft^3 × 32.2 ft/s^2) × sin(15°). Multiplying the pressure gradient by the wellbore length of 6,000 ft gives the potential pressure drop.

b) To determine the frictional pressure drop in the wellbore, we can use the Darcy-Weisbach equation. The Darcy-Weisbach equation states that the pressure drop is equal to the friction factor multiplied by the pipe length, density, squared velocity, and divided by the pipe diameter. However, to calculate the friction factor, we need the Reynolds number. The Reynolds number can be calculated as (density × velocity × diameter) divided by the oil viscosity. Once the Reynolds number is known, the friction factor can be determined. Finally, using the friction factor, we can calculate the frictional pressure drop.

c) To calculate the in-situ oil velocity, we need to consider the total volume of the pipe, including both oil and gas. The total pipe volume is calculated as the pipe cross-sectional area multiplied by the wellbore length. Subtracting the gas volume from the total volume gives the oil volume. Dividing the oil volume by the total time taken by the oil to flow through the pipe (converted to seconds) gives the average oil velocity.

d) The flow regime of the two-phase flow can be determined based on the oil and gas mixture properties and flow conditions. Common flow regimes include bubble flow, slug flow, annular flow, and mist flow. These regimes are characterized by different distribution and interaction of the oil and gas phases. To determine the specific flow regime, various parameters such as gas and liquid velocities, mixture density, viscosity, and surface tension need to be considered. Additional information would be required to accurately determine the flow regime in this scenario.

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In summary: Mean (μ): 120, Standard deviation (σ): 6.93, Minimum usual value (μ - 2σ): 106.14 and Maximum usual value (μ + 2σ): 133.86

To find the mean mu μ of the binomial distribution, we use the formula mu = n*p. Therefore, mu = 200*0.6 = 120.

To find the standard deviation sigma σ, we use the formula sigma = sqrt(n*p*(1-p)). Therefore, sigma = sqrt(200*0.6*0.4) = 6.93.

Using the range rule of thumb, we can estimate the minimum usual value by subtracting 2 times the standard deviation from the mean, and the maximum usual value by adding 2 times the standard deviation to the mean. Therefore, the minimum usual value is mu - 2*sigma = 120 - 2*6.93 = 106.14, and the maximum usual value is mu + 2*sigma = 120 + 2*6.93 = 133.86.

So, in summary, the mean mu μ of the binomial distribution is 120, the standard deviation sigma σ is 6.93, the minimum usual value mu minus 2 sigma μ−2σ is 106.14, and the maximum usual value mu plus 2 sigma μ+2σ is 133.86.
For a binomial distribution, the mean (μ) and standard deviation (σ) can be calculated using the formulas:

μ = n * p
σ = √(n * p * (1 - p))

Given n = 200 and p = 0.6, we can find μ and σ:

μ = 200 * 0.6 = 120
σ = √(200 * 0.6 * (1 - 0.6)) = √(200 * 0.6 * 0.4) = √48 ≈ 6.93

Next, we can use the range rule of thumb to find the minimum and maximum usual values:

Minimum usual value (μ - 2σ):
120 - (2 * 6.93) = 120 - 13.86 ≈ 106.14

Maximum usual value (μ + 2σ):
120 + (2 * 6.93) = 120 + 13.86 ≈ 133.86

In summary:
Mean (μ): 120
Standard deviation (σ): 6.93
Minimum usual value (μ - 2σ): 106.14
Maximum usual value (μ + 2σ): 133.86

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Answer:

  $11.40

Step-by-step explanation:

You want to know the mom's total spending if she bought ...

using a $0.50 discount coupon.

The total bill is the sum of the costs of the items, less the amount of the discount coupon:

  $4.25 +2×2.25 +3.15 -0.50 = $11.40

She spent $11.40 at the coffee shop.

<95141404393>

Answer:

11.40

Step-by-step explanation:

Your welcome!

Answer: 12/48 = 25%

Step-by-step explanation: If the unit rate that characterizes my juice reflects its concentration, then there are 36 + 12 = 48 ounces of matter in total. The orange juice mix that we add is 12 ounces of mix, therefore the concentration is 12/48 = 25%.