Mark Went to the store and purchase nine pairs of socks and three packages of undershirts for $8.28 each he also purchase a pair of pants for $32 he spent a total of $77.99 how much did he pay for each pair of socks write an equation using the variable S

Answer:

y  = 0.70x-  10.00

Step-by-step explanation:

--  Since one friend gave you 10.00 ,subtractthis from the 13.50 to give you the amount earned by walking the 5 miles

--  13.5-10.00  =  $3.50  

--  Since you walked 5 miles, divide by 5 to give you 0.70 per mile earned.

So, an equation that represents the amount of money earned is:  

y  = 0.70x-  10.00  . This is in slope-intercept form; the slope is $0.70 and represents the amount of money earned per mile  and the intercept is $10.00 and represents the initial amount of money that you were given.

Answer:

x = 30/48 or x = 0.625

Step-by-step explanation:

3/2 = 4/3x + 2/3

Convert to common denominator

9/6 = 8/6x + 4/6

subtract 4/6 from both sides

9/6 - 4/6 = 8/6x + 4/6 - 4/6

5/6 = 8/6x

Divide by 8/6

5/6 x 6/8 = x

30/48 = x

x = 30/48

If my answer is incorrect, pls correct me!

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-Chetan K

According to the property of parallelogram, Angle ABC is right angle.

Given:In □ABCD is quadrilateral

AB=DC andAD=BC

To prove: Angle ABC is right angle

Proof: in △ABC and △ADC

AD=BC [Given]

AB=DC [Given]

AC=AC [Common side]

thus, By SSS property △ADC≅△ACB

∴∠DAC=∠DCA

∴AB∣∣DC

In△ABD and △DCB

DB=DB [Common side]

AD=BC [Given]

AB=DC [Given]

Thus, △ABD≅△DCB

AD∣∣BC

Since AB∣∣DC and AD∣∣BC, △ABCD is parallelogram

Therefore, Angle ABC is right angle.

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According to the information we can infer that the approximate area of the cross-section is 35.5 square meters. Additionally, the approximate volume of water flowing through the cross-section in 10 seconds is 142 cubic meters.

To calculate the approximate area of the cross-section using Simpson's rule, we divide the width of the river (12 meters) into intervals and consider the depth measurements at each interval. Given the depth measurements:

We use Simpson's rule to estimate the area by applying the formula:

Using the given depth measurements, we substitute them into the formula and calculate:

According to the information, the approximate area of the cross-section is 35.5 square meters.

To calculate the approximate volume of water flowing through the cross-section in 10 seconds, we multiply the area of the cross-section by the velocity of the river.

Given the velocity of the river is 0.4 meters per second, and the time is 10 seconds:

According to the information, the approximate volume of water flowing through the cross-section in 10 seconds is 142 cubic meters.

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Answer:    53.213

Step-by-step explanation:

Given the differential equation dy/dx = y(8x^2+1)We have to find the general solution of the given differential equation and express it explicitly as a function of the independent variable.

We can solve this differential equation by the method of separating variables. Let's start solving. \(dy/dx = y(8x^2+1)Divide both sides by y(8x^2+1)\).So, we get\(1/y dy = (8x^2+1) dx\)Integrating both sides, we get\(∫ 1/y dy = ∫ (8x^2+1) dx On integrating, we get ln |y| = (8/3)x^3 + x + C\) where C is an arbitrary constant of integration.

Raise e to both sides, we \(get |y| = e^(8/3)x^3+xe^CNow, |y| = e^(8/3)x^3.e^C\)On putting a positive constant of integration, we can write |y| = Ke^(8/3)x^3 where K is a positive constant of integration. Since |y| can be either positive or negative, therefore,\(y = ±Ke^(8/3)x^3\)Therefore, the general solution of the given differential equation is\(y = Ke^(8/3)x^3\)where K is a positive constant of integration.

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The number of dimes Hailey has is 29 dimes.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 8 is an equation.

We have,

Number of dimes = x

Number of quarters = y

Now,

1 dime = $0.10

1 quarter = $0.25

We can make two equations.

x + y = 65 ____(1)

x = 65 - y _____(2)

0.10x + 0.25y = 11.90 ______(3)

Now,

Substituting (2) in (3).

0.10 (65 - y) + 0.25y = 11.90

6.5 - 0.10y + 0.25y = 11.90

6.5 + 0.15y = 11.90

0.15y = 11.90 - 6.5

0.15y = 5.4

y = 36

And,

x = 65 - y

x = 65 - 36

x = 29

Thus,

Hailey has 29 dimes.

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An isosceles triangle with two long sides and a short bottom side can have infinitely many possible congruent triangles. However, assuming that the two long sides have a fixed length of 1 unit and the length of the short bottom side is less than 1 unit, there are only two possible congruent triangles.

One of the congruent triangles would have angles of approximately 22.62°, 22.62°, and 135.76°, while the other congruent triangle would have angles of approximately 157.38°, 11.25°, and 11.25°. Therefore, the answer to this question depends on the specific length of the short bottom side and the context of the problem.

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X + 1 = 1.5, X - 1 = -0.5, 2X = 1, \(X^2\) = 0.25, 1/X = 2, X × 2 = 1, X/2 = 0.25, √(X) = 0.707, log(X) = -0.301, sin(X) = 0.479

Here are some mathematical expressions related to the equation X = 1/2:

X + 1 = 1/2 + 1

X - 1 = 1/2 - 1

2X = 2 × (1/2)

\(X^2 = (1/2)^2\)

1/X = 1/(1/2)

X × 2 = (1/2) × 2

X/2 = (1/2)/2

√(X) = √(1/2)

log(X) = log(1/2)

sin(X) = sin(1/2)

These expressions manipulate or relate to the value of X, which is equal to 1/2.

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The mode of a dataset is the value that appears most frequently. In this case, we need to find the interval of rainfall that occurs most frequently.

From the given data, we can see that the interval "less than 0.01 inch" has the highest frequency with 165 days. Therefore, the mode of this dataset is "less than 0.01 inch"

Effective communication is crucial in all aspects of life, including personal relationships, business, education, and social interactions. Good communication skills allow individuals to express their thoughts and feelings clearly, listen actively, and respond appropriately. In personal relationships, effective communication fosters mutual understanding, trust, and respect.

In the business world, it is essential for building strong relationships with clients, customers, and colleagues, and for achieving goals and objectives. Good communication also plays a vital role in education, where it facilitates the transfer of knowledge and information from teachers to students.

Moreover, effective communication skills enable individuals to engage in social interactions and build meaningful connections with others. Therefore, it is essential to develop good communication skills to succeed in all aspects of life.

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Answer:

-1

Step-by-step explanation:

\(\boxed{\begin{minipage}{4.4cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\\\end{minipage}}\)

Define two points on the line:

Substitute the defined points into the slope formula:

\(\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-2-0}{0-(-2)}=\dfrac{-2}{2}=-1\)

Therefore, the slope of the line is -1.

Answer:

  26, 11, 4, 5, 14

Step-by-step explanation:

To find the value of the function, replace the variable with the number and do the arithmetic.

  f(-2) = 4(-2)² -3(-2) +4 = 16 +6 +4 = 26

For doing repetitive calculations, it is convenient to write the formula into a calculator or spreadsheet and let it work from the list of values. That is what we did in the attached. It shows a table of x and f(x) for the values of x you are interested in.

The function values are ...

_____

Additional comment

For evaluating polynomials, either by hand or machine, it is often convenient to rewrite the polynomial in Horner Form. The total number of math operations tends to be reduced. When doing this by hand, the arithmetic tends to be easier.

  f(x) = (4x -3)x +4

That is, the powers of x accumulate as each layer in parentheses is multiplied by x and the next coefficient added to the result.

Using this form, ...

  f(-1) = (4(-1) -3)(-1) +4

  f(-1) = (-7)(-1) +4 = 11

Answer:

what?

Step-by-step explanation:

Answer:

m<a is 32º

Step-by-step explanation:

4x-8=2x+12

   +8       +8

4x=2x+20

-2x     -2x

2x=20

÷2

x=10

4x-8

4(10)-8

40-8

32

Answer

20

Step-by-step explanation: Divide 200 to 10

The number of weeks after which there will be no money left in the account is 20 weeks.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Initial amount = $200

Amount withdrawn each week = $10

The number of weeks after which there will be no money.

Weeks = x

200 - 10x = 0

200 = 10x

x = 200 / 10

x = 20

Thus,

The number of weeks is 20.

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Area del triangulo = base por altura/2

A = b*h/2    

A = 22,5cm²

Base = 5cm

a = b*h/2

22,5cm² = 5cm /h

22,5cm²/5cm = h

4,5cm = h

What is Area del?

Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

La altura del triangulo es de 4,5cm

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Both the limits are equal to -1, which means the function is continuous at x=1. Therefore, there is no discontinuity at x=1. So, The function is continuous at x=1.

To determine if the function is continuous at x=1, we need to evaluate the left and right limits of the function at x=1 and see if they are equal.

Left limit as x approaches 1:

\lim_{x\to 1^-}\frac{2x^2-5x+3}{x-1} = \frac{2(1)^2-5(1)+3}{1-1} = \frac{0}{0}

Right limit as x approaches 1:

\lim_{x\to 1^+}\frac{2x^2-5x+3}{x-1} = \frac{2(1)^2-5(1)+3}{1-1} = \frac{0}{0}

Since both limits are indeterminate forms of 0/0, we can use L'Hopital's Rule to evaluate them.

Taking the derivative of the numerator and denominator of the original function, we get:

\lim_{x\to 1^-}\frac{4x-5}{1} = -1

\lim_{x\to 1^+}\frac{4x-5}{1} = -1

Both limits are equal to -1, which means the function is continuous at x=1. Therefore, there is no discontinuity at x=1.

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The values of functions are:

a) f( x ) + g( x ) = x² + x - 3

b) f( x ) - g( x ) = x² - x - 5

c) f( x ) / g( x ) = x² - 4/ (x+ 1)

d) f( x ) * g( x ) = x³ + x² - 4x - 4

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. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

f(x) = x² - 4 and g (x) = x + 1  

a) f( x ) + g( x )

= x² - 4  + x+ 1

= x² + x - 3

b) f( x ) - g( x )

=  x² - 4 - ( x+ 1)

=  x² - 4 - x- 1

= x² - x - 5

c) f( x ) / g( x )

=  x² - 4/ (x+ 1)

d) f( x ) × g( x )

= (x²- 4)( x+ 1)

= x³ + x² - 4x - 4

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The displacement of an object undergoing simple harmonic motion with a period of 7 minutes and an amplitude of 12 m can be modeled by the equation d = 12 sin((2π/7) f), where d represents the displacement and f is the time in minutes.

In simple harmonic motion, the displacement of an object can be represented by a sinusoidal function. The general equation for displacement as a function of time in simple harmonic motion is given by d = A sin(2π/T) f, where A is the amplitude, T is the period, and f is the time.

In this case, the period of the motion is 7 minutes, and the amplitude is 12 m. Thus, we can substitute these values into the general equation to obtain d = 12 sin((2π/7) f).

The negative displacement of -12 m at time f = 0 minutes indicates that the object is at its maximum displacement in the negative direction at the start. Since the equation represents a sinusoidal function, the initial positive direction of motion can be determined by examining the phase of the sine function at f = 0. In this case, the displacement is negative, which implies a phase shift of half a period (180 degrees or π radians) to account for the initial position. Therefore, the object is moving in the positive direction at the start.

In conclusion, the equation modeling the displacement d as a function of time f for the given simple harmonic motion is d = 12 sin((2π/7) f), where d represents the displacement and f is the time in minutes.

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Answer:

27/64 I think...maybe

Step-by-step explanation:

Answer:

 -y • (6x^2 + 3xy - 4)

Step-by-step explanation:

At μ = 10.0932 level should the mean be set if it is required that only 1% of the bags weigh less than 9.5 kg.

Given Data:

σ = 0.04 kg

x = 9.5 kg

We want to determine μ such that: P(X ≤ 9.5)= 1% = 0.01

Thus, we know here probability of x is 0.1 which is  less than 9.5

so here Z is -2.326 by the standard table

Determine the z-score in the normal probability table in the appendix that has a probability closest to 0.01:

Then, we have here 1% to left when Z is - 2.326

Now,

The value corresponding to the z-score is then the mean increased by the product of the z-score and the standard deviation:

x = μ+ zσ

= μ− 2.33(0.04) = μ - 0.0932

Since , P(X ≤ 9.5) = 0.95% = 0.095, we know that x also has to be equal to 9.5:

   μ− 0.0932 = 9.5

Add 0.0932 to each side of the previous equation:

μ = 10+ 0.0932

= 10.0932

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The probability of this event of getting a queen when selecting 49 cards from a shuffled deck is represented by a value of 1.

The probability of an occurrence can be determined using the probability formula by only dividing the favorable number of possibilities by the entire number of possible outcomes.

Given that the favorable number of outcomes can never exceed the total number of outcomes, the chance of an event occurring can range from 0 to 1. Therefore, there cannot be any unfavorable outcomes.

In the given question,

Out of 52 cards in the deck, when selecting 49 cards the event of getting a queen is only once.

The likelihood of an occurrence that is regarded as certain, or absolutely certain to occur, is 100% = 1.

The 49 cards you choose from a shuffled deck will all be queens, so you can be sure of that.

This indicates that a value of 1 represents the probability of this event.

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Answer:

-6

Step-by-step explanation:

By looking at the graph, you can see that the graph intersects the x-axis at (-6,0), that is the zero of g.

Answer:

-9

Step-by-step explanation:

The graph's y-intercept is -9, which is the zero of g.

Answer;

They will be 0.5x miles away from each other

Explanation;

Since the dog runs twice the speed of the cat

Its speed will be 2 * x = 2x mph

Now we want to know how far they will be from each other after 30 minutes

Kindly note that 30 minutes is 1/2 hour

Mathematically;

distance = speed * time

Distance of cat = x * 1/2 = 0.5x miles

Distance of dog = 2x * 0.5 = x miles

The dog is x - 0.5x miles = 0.5x miles away from the cat

They will be 0.5x miles away from each other.

Since Bobby's cat runs x mph. Bobby's dog runs twice as fast as his cat.

So here the speed of the dog should be 2x

Now we know that

\(Distance = speed \times time\\\\\)

Here distance of cat should be x of 30 minutes or half hour = 0.5x miles

And, Distance of dog should be 2x of 0.5 = x miles

So, the difference should be

= x - 0.5

= 0.5x miles

hence, They will be 0.5x miles away from each other.

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The correct answer to the above threads-based question Option is d. 1/6 inch.

The phrase "12 threads per inch" refers to the number of ridges or threads on the screw shaft for every inch of its length. This indicates that the space between two consecutive threads for a single thread is 1/12 inch.

When the screw turns two complete revolutions, it travels a distance equal to the screw pitch. The spacing between neighboring threads is specified as the screw pitch. Because there is just one thread in this scenario, the pitch is 1/12 inch.

When the screw completes two complete rotations, it advances into the nut a distance equal to the screw pitch, which is 1/12 inch. Since the answer choices are given in fractions, we can simplify 1/12 to 1/6 by dividing both the numerator and denominator by 2. Hence, the correct answer is d) 1/6 inch.

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The correct answer to the above threads-based question Option is d. 1/6 inch.

The phrase "12 threads per inch" refers to the number of ridges or threads on the screw shaft for every inch of its length. This indicates that the space between two consecutive threads for a single thread is 1/12 inch.

When the screw turns two complete revolutions, it travels a distance equal to the screw pitch. The spacing between neighboring threads is specified as the screw pitch. Because there is just one thread in this scenario, the pitch is 1/12 inch.

When the screw completes two complete rotations, it advances into the nut a distance equal to the screw pitch, which is 1/12 inch. Since the answer choices are given in fractions, we can simplify 1/12 to 1/6 by dividing both the numerator and denominator by 2. Hence, the correct answer is d) 1/6 inch.

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The measure of arc BC is 720 times the measure of angle BAC.

Given that AC is the diameter of the circle and AB is a chord with a length of 16 units, we need to find BC (the length of the other chord) and mBC (the measure of angle BAC).

To find BC, we can use the property of chords in a circle. If two chords intersect within a circle, the products of their segments are equal. In this case, since AB = BC = 16 units, the product of their segments will be:

AB * BC = AC * CE

16 * BC = 2 * r * CE (AC is the diameter, so its length is twice the radius)

Since the area of the circle is given as 289 square units, we can find the radius (r) using the formula for the area of a circle:

Area = π * r^2

289 = π * r^2

r^2 = 289 / π

r = √(289 / π)

Now, we can substitute the known values into the equation for the product of the segments:

16 * BC = 2 * √(289 / π) * CEBC = (√(289 / π) * CE) / 8

To find mBC, we can use the properties of angles in a circle. The angle subtended by an arc at the center of a circle is double the angle subtended by the same arc at any point on the circumference. Since AC is a diameter, angle BAC is a right angle. Therefore, mBC will be half the measure of the arc BC.

mBC = 0.5 * m(arc BC)

To find the measure of the arc BC, we need to find its length. The length of an arc is determined by the ratio of the arc angle to the total angle of the circle (360 degrees). Since mBC is half the arc angle, we can write:

arc BC = (mBC / 0.5) * 360

arc BC = 720 * mBC

Therefore, the length of the arc BC equals 720 times the length of the angle BAC.

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(a) Example question: "How often do you look at social media while doing schoolwork?

(b) Sofie can select a simple random sample of students by using a random number generator to assign a unique identification number to each student in the online high school.

(c) The sample for Sofie's research is the 32 completed surveys she received. These surveys represent the responses of a subset of the population. The population, in this case, refers to all the students at the online high school.

(d) If Sofie uses only the completed surveys, she can conclude that approximately 50% (16 out of 32) of the students who completed the survey reported using social media while doing schoolwork.

(a) Please select one of the following options: never, rarely, occasionally, frequently, or always."

(b) She can then use the random number generator again to select a specific number of students from the entire population of students, ensuring that each student has an equal chance of being selected. For example, if there are 500 students in total and Sofie wants a sample size of 50, she can generate 50 random numbers and select the corresponding students based on their identification numbers.

(d) However, it is important to note that this conclusion is specific to the sample of completed surveys and cannot be generalized to the entire population of high school students.

To make an inference about the percent of all high school students who use social media while doing schoolwork, Sofie would need a larger and more representative sample that covers a wider range of students in the online high school.

Additionally, she should consider potential biases in the sample, such as non-response bias if the students who chose not to complete the survey have different social media usage patterns compared to those who did respond.

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Answer:

Local Maximum Approx.: (1,8.08)

Local Minima Approx.: (-2,-7.67) and (3,2.75)

Step-by-step explanation:

Local maximums and minima there the highest and lowest points, respectively, on a graph in a specific region. (This is different from absolute maximum and minimum, which are the highest and lowest points overall.)

These are pretty clear to see on a curve, as they are the "turns" or the points where the curve switches direction from up to down or down to up.

On your graph, we have two local minima and one local maximum. The local minima are at x= -2 and x=3. The local maximum is at x=8. Because of the way the graph is, we have to approximate the y-values of each point.

The answer option which best describes this is the third option, so that is your answer.