A cell phone is on sale for $205 after a 20% off discount. What was the original price of the phone?

The required Matlab code to find the greatest common divisor of a number using the Euclidean algorithm is shown.

To find the greatest common divisor (GCD) of two numbers using the Euclidean algorithm in MATLAB, you can use the following code:

% Replace '12345678' with your actual student number

studentNumber = '12345678';

% Extract the first 4 digits as the first number

firstNumber = str2double(studentNumber(1:4));

% Extract the last 3 digits as the second number

secondNumber = str2double(studentNumber(end-2:end));

% Find the GCD using the Euclidean algorithm

gcdValue = gcd(firstNumber, secondNumber);

% Display the result

disp(['The GCD of ' num2str(firstNumber) ' and ' num2str(secondNumber) ' is ' num2str(gcdValue) '.']);

Make sure to replace '12345678' with your actual student number. The code extracts the first 4 digits as the first number and the last 3 digits as the second number using string indexing. Then, the gcd function in MATLAB is used to calculate the GCD of the two numbers. Finally, the result is displayed using the disp function.

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Wilson and William were measured at various times, therefore drawing the inference that Wilson grew more over the course of a year than William is incorrect and the statistics is misleading.

Inferential statistics and descriptive statistics are two disciplines of statistics with distinct applications.

Summarizing and characterizing gathered data is the focus of descriptive statistics. It uses techniques including graphical presentations, measurements of variability, and measures of central tendency, such as mean, median, and mode (e.g., histograms, box plots). The purpose of descriptive statistics is to shed light on a sample's or population's properties, such as its distribution, dispersion, and shape.

Wilson and William were measured at various times, therefore drawing the inference that Wilson grew more over the course of a year than William is incorrect.

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The correct answer is: (4, 3) is a member. Its cardinality is 4.

Matching the sets on the left with a true statement about the Cartesian product of those sets on the right:{1, 2} × {3, 4} = {(1, 3), (1, 4), (2, 3), (2, 4)}{1, 2, 3, 4} × {3, 4, 5, 6} = {(1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 3), (3, 4), (3, 5), (3, 6), (4, 3), (4, 4), (4, 5), (4, 6)}{4, 5, 6, 7} × {4, 5, 6, 7} = {(4, 4), (4, 5), (4, 6), (4, 7), (5, 4), (5, 5), (5, 6), (5, 7), (6, 4), (6, 5), (6, 6), (6, 7), (7, 4), (7, 5), (7, 6), (7, 7)}{a, e, i, o, u} × {b, g, t, d} = {(a, b), (a, g), (a, t), (a, d), (e, b), (e, g), (e, t), (e, d), (i, b), (i, g), (i, t), (i, d), (o, b), (o, g), (o, t), (o, d), (u, b), (u, g), (u, t), (u, d)}{1, 2, 3} × {1, 2, 4} = {(1, 1), (1, 2), (1, 4), (2, 1), (2, 2), (2, 4), (3, 1), (3, 2), (3, 4)}The following are true statements about the Cartesian product of these sets:its cardinality is 4. (4, 3) is a member.

Therefore, the correct answer is: (4, 3) is a member. Its cardinality is 4.

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Answer:

\({ \rm{y = - 3x + 5}}\)

Gradient = -3

• Parallel lines have the same gradient, therefore gradient, m is -3

\({ \rm{y = mx + c}}\)

• At point (0, -4)

\({ \rm{ - 4 = ( - 3 \times 0) + c}} \\ \\ { \rm{c = - 4}}\)

y intercept is -4

\({ \boxed{ \boxed{ \mathfrak{answer : }}{ \rm{\: \: y = - 3x - 4}}}}\)

Answer:

above answer is correct

mrk that braniliest

Answer:

165 km

Step-by-step explanation:

We know the ratio of map distance to actual distance is 1 cm : 15 km

Multiplying both sides by 11, we have 11 cm : 165 km

Answer:

What do you need help with

Step-by-step explanation:

Answer:

7

3 times ? - 11

=

? + 3

? = 7

Step-by-step explanation:

3 times 7 is 21 -11 is 10

7+3 is 10

Both equations has to make 10 so it is the answer of 7

Hope this helps :)

Answer:

\(\boxed{x=7 }\)

Step-by-step explanation:

3x - 11 = x + 3

→ Minus x from both sides to isolate the 'x's

2x - 11 = 3

→ Add 11 to both sides to isolate 2x

2x = 14

→ Divide both sides 2 to isolate x

x = 7

Answer: Steph is 16 today

Step-by-step explanation:

Austin age today = x

Austin in 4 years = x+4

Steph age today = 4x (because Austin is 1/4 her age today)

Steph age in 4 years is 4x + 4

In 4 years Austin's age is 2/5 of Steph's, so:

2/5 (x+4) = 4x + 4

Now solve for x!

x+4 = (8/5)x + 8/5

12/5 = (3/5)x

Therefore Austin is 4 years old today (x=4) and...

Steph age today = 4x = 4x4 = 16

Answer: See Bellow

Step-by-step explanation:

Juliet's sample may not be valid for several reasons. Firstly, her sample size of 20 students may not represent the entire student population at her school. If her class is not a random sample of the whole student population, her results may not generalize to the entire school. Additionally, the model may suffer from selection bias if she only surveyed students she knew liked short stories or if she conducted the survey in a way that only sure students responded. Therefore, it is essential to have a large and representative sample to ensure the validity of the conclusions drawn from the survey results.

Answer: 16%

Step-by-step explanation:

1. 60% not working = 40% working

2. 40% ^ 2, or 40% x 40% = 16%

Answer : value of x and y in the matrix equation is:

x = -3

y = +4, -4

Step-by-step explanation :

The matrix expression is:

\(\left[\begin{array}{ccc}x+4\\y^2+1\end{array}\right]+\left[\begin{array}{ccc}-9x\\-17\end{array}\right]=\left[\begin{array}{ccc}28\\0\end{array}\right]\)

First we have to add left hand side matrix.

\(\left[\begin{array}{ccc}(x+4)+(-9x)\\(y^2+1)+(-17)\end{array}\right]=\left[\begin{array}{ccc}28\\0\end{array}\right]\)

Now we have to add left hand side terms.

\(\left[\begin{array}{ccc}x+4-9x\\y^2+1-17\end{array}\right]=\left[\begin{array}{ccc}28\\0\end{array}\right]\)

\(\left[\begin{array}{ccc}4-8x\\y^2-16\end{array}\right]=\left[\begin{array}{ccc}28\\0\end{array}\right]\)

Now we have to equating left hand side matrix to right hand matrix, we get:

\(\Rightarrow 4-8x=28\text{ and }y^2-16=0\\\\\Rightarrow 8x=4-28\text{ and }y^2=16\\\\\Rightarrow x=-3\text{ and }y=\pm 4\)

Therefore, the value of x and y in the matrix equation is -3 and +4, -4 respectively.

Answer:

D is wrong. The correct answer choice is C ( x=-3 and y= +4, -4)

Step-by-step explanation:

Math unit test review

Answer:

B. 81 in.²

Step-by-step explanation:

We have been given that the trapezoid shown in the attachment has been enlarged by a scale of 1.5. We are asked to find the area of the enlarged trapezoid.

The area of the original trapezoid is 36 square inches.

Since each side of the trapezoid is enlarged 1.5 times, so the area of new trapezoid would be 2.25 times greater than area of original trapezoid.

The area would be 2.25 times greater because area is product of sum of lengths of parallel sides and height.

1.5 × 1.5 = 2.25

Area of new trapezoid: 2.25 × 36 in²

Area of new trapezoid = 81 in²

The area of the enlarged trapezoid would be 81 in² or option B.

Answer:

31 1/2

Step-by-step explanation:

average speed = distance/time

average speed = (73 1/2 miles)/(2 1/3 hours)

= (147/2 miles)/(7/3 hours)

= 147/2 * 3/7 miles/hour

= 441/14 miles/hour

= 31 1/2 miles/hour

Answer:

11/20

Step-by-step explanation:

5 cents is worth $0.05.

A quarter is worth $0.25.

A dime is worth $0.10

A nickel is worth $0.05

A penny is worth $0.01

In total there are 40 coins in the jar.

The coins that are worth more than $0.05 dollars are the dimes and quarters, so there are 22 coins worth more than $0.05.

Therefore, the probability of of picking a coin worth more than 5 cents is:

22 / 40 = 11/20

Answer:

A

Step-by-step explanation:

Answer:

D. the exponent can be odd

Step-by-step explanation:

A. (-4)² = 16 ⇒ -4 is even and the product is positive.

B. (-5)² = 25 ⇒ -5 is odd and the product is positive.

C. (-5)⁴ = 625 ⇒ The exponent 4 is even and the product is positive.

D. (-5)⁵ = -3125 ⇒ The exponent 5 is odd and the product is negative.

So, the answer is D.

Hope this helps.

The box plot would show the distribution of Tori's training runs and provide insights into the Central tendency and variability of the data.

A box plot, also known as a box-and-whisker plot, is a visual representation of the distribution of a dataset. It shows the median, quartiles, and range of the data. The median is the middle value of the dataset, the first quartile is the value that separates the lowest 25% of the data from the rest, and the third quartile is the value that separates the lowest 75% of the data from the rest. The range is the distance between the minimum and maximum values of the data.

To create a box plot for Tori's training runs, you would first order the data from smallest to largest: 6, 7, 8, 8, 11, 12, 13, 15, 16, 16, 20. Then, you would find the median (the middle value), which is 12.5. Next, you would find the first quartile (the value that separates the lowest 25% of the data from the rest), which is 8, and the third quartile (the value that separates the lowest 75% of the data from the rest), which is 16. Finally, you would calculate the range (the distance between the minimum and maximum values), which is 14 (20 - 6).

To draw the box plot, you would draw a rectangle with the bottom edge at the first quartile and the top edge at the third quartile. Inside the rectangle, draw a line at the median. Then, draw whiskers (lines) from the edges of the rectangle to the minimum and maximum values of the data (6 and 20). Any outliers (values that are more than 1.5 times the interquartile range away from the nearest quartile) can be plotted as individual points outside of the whiskers.

Without a visual representation of the data, it is difficult to say which box plot represents the data. However, the box plot would show the distribution of Tori's training runs and provide insights into the central tendency and variability of the data.

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In general, a change in the price of the product causes a movement along the demand curve; and a change in production cost and related factors causes a shift in the supply curve.

The demand curve is a graphical representation of the relationship between the price of a good or service and the quantity demanded for a given period of time. In a typical representation, the price will appear on the left vertical axis of the graph, and the quantity demanded on the horizontal axis.

The supply curve is a graphic representation of the relationship between product price and quantity of product which a seller is willing and able to supply. Product price is measured on the vertical axis of the graph, and the quantity of product supplied on the horizontal axis.

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The constant of variation is 13.

The value of y when x is 15 is 195.

Direct variation is when two values move in the same direction. If one variable increases, the other variable increases.

The equation that represents direct variation is:

y = kx

Where:

91 = 7k

k = 91 / 7

k = 13

The value of y when x = 15

y = 13 x 15

y = 195

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Answer: I think D IM GUESSING

Step-by-step explanation:

I think D cuz It has McDonald's in it and I'm lovin' it... Jk

Answer:

The answer is D

Step-by-step explanation:

When selecting a single score from a population with a mean of 100 and a standard deviation of 20, we can expect, on average, the selected score to be approximately 20 units away from the population mean.

The population mean (μ) is a measure of the average or central tendency of the population, while the population standard deviation (σ) is a measure of the variability or spread of the scores in the population. In this case, the population mean is 100 and the population standard deviation is 20.

When we select a single score from the population, we can expect it to be, on average, close to the population mean. This is because the population mean represents the center or average value of the population.

The standard deviation provides us with a measure of the dispersion or spread of scores around the mean. A standard deviation of 20 indicates that the scores in the population tend to deviate from the mean by an average of 20 units.

Considering that the standard deviation represents the average distance between individual scores and the mean, we can conclude that, on average, a single score selected from the population would be approximately 20 units away from the population mean.

However, it is important to note that this is a probabilistic statement. While the average distance between individual scores and the mean is expected to be 20 units, there will be some scores that are closer to the mean and others that are further away.

The distribution of scores in the population follows a bell-shaped curve (assuming a normal distribution), and the majority of scores will fall within a few standard deviations from the mean.

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Note the full question is A population has μ = 100 and σ = 20. If you select a single score from this population, on the average, how close would it be to the population mean? Explain your answer.

Answer:

             The x intercept:    (1.5, 0)

The slope intercept form:   y = 2x - 3

                      The slope:    m = 2

Step-by-step explanation:

x intercept means y=0

4x - 2y = 6

4x - 2·0 = 6

4x = 6

x = 1.5

The slope intercept form is:  y = mx + b

4x - 2y = 6            {subtract 4x from both sides}

- 2y = - 4x + 6       {dividing both sides by (-2)}

y = 2x - 3            ← slope intercept form

Slope is the number by x, in slope intercept form of line's equation

Answer:

a = 3

Step-by-step explanation:

Since x = 7 is a solution, substitute x = 7 into the equation and solve for a

4(7) - 2(7 + a) = 8 , that is

28 - 2(7 + a) = 8 ( subtract 28 from both sides )

- 2(7 + a) = - 20 ( divide both sides by - 2 )

7 + a = 10 ( subtract 7 from both sides )

a = 3

Answer:

g(x) = x² - 4 is already in form of a variable, I.e., x

g(4x) takes another variable, I.e., 4x

Same as before, 4x takes over x:

=> g(4x) = (4x)² - 4

=> g(4x) = 16x² - 4

OR

=> g(4x) = 4{4x² - 1}

\(\large{\rm{\underline{\underline{Answer:}}}}\)

Now we have g(4x). This means, we have to replace x by 4x and correspondence to this, the equation will change. I.e.

⇛ g(4x) = (4x)² - 4

⇛ g(4x) = 16x² - 4 / 4(4x² - 1) [answer]

Answer:

5(2)+5(7)

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

First multiply inside of the parenthesis with 3 then add the like terms

3x + 6 - 6 = 15 ➡ 3x = 15 divide both sides with 3 and x = 5

The dimensions that will result in a solid with maximum volume are approximately x = 12.02 centimeters and h = 5.01 centimeters.

Let the side of the square base be x, and let the height of the rectangular solid be h. Then, the surface area of the solid is given by:

Surface area = area of base + area of front + area of back + area of left + area of right

Surface area = x² + 2xh + 2xh + 2xh + 2xh = x² + 8xh

We are given that the surface area is 433.5 square centimeters, so we can write: x² + 8xh = 433.5

We want to find the dimensions that will result in a solid with maximum volume. The volume of the solid is given by:

Volume = area of base × height = x² × h

We can use the surface area equation to solve for h in terms of x:

x² + 8xh = 433.5

h = (433.5 - x²)/(8x)

Substituting this expression for h into the volume equation, we get:

Volume = x² × (433.5 - x²)/(8x) = (433.5x - x³)/8

To find the maximum volume, we need to find the value of x that maximizes this expression. To do this, we can take the derivative of the expression with respect to x, set it equal to zero, and solve for x:

d(Volume)/dx = (433.5 - 3x²)/8 = 0

433.5 - 3x² = 0

x² = 144.5

x = sqrt(144.5) ≈ 12.02

We can check that this is a maximum by computing the second derivative of the volume expression with respect to x:

d²(Volume)/dx² = -3x/4

At x = sqrt(144.5), this is negative, which means that the volume is maximized at x = sqrt(144.5).

Substituting x = sqrt(144.5) into the expression for h, we get:

h = (433.5 - (sqrt(144.5))²)/(8×sqrt(144.5))

h = 433.5/(8×sqrt(144.5)) - sqrt(144.5)/8

h = 5.01

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The dimensions of the rectangular solid that will result in a maximum volume are approximately.\(6.34 cm \times 9.03 cm \times 9.03 cm.\)

Let's assume that the length, width, and height of the rectangular solid are all equal to x, so the base of the solid is a square.

The surface area of the rectangular solid can be expressed as:

\(SA = 2xy + 2xz + 2yz\)

Substituting x for y and z, we get:

\(SA = 2x^2 + 4xy\)

We are given that the surface area is 433.5 square centimeters, so:

\(2x^2 + 4xy = 433.5\)

Simplifying, we get:

\(x^2 + 2xy - 216.75 = 0\)

Using the quadratic formula to solve for y, we get:

\(y = (-2x\± \sqrt (4x^2 + 4(216.75)))/2\)

\(y = -x \± \sqrt (x^2 + 216.75)\)

Since the base of the rectangular solid is a square, we know that y = z. So:

\(z = -x \± \sqrt(x^2 + 216.75)\)

The volume of the rectangular solid is given by:

\(V = x^2y\)

Substituting y for\(-x + \sqrt (x^2 + 216.75),\) we get:

\(V = x^2(-x + \sqrt(x^2 + 216.75))\)

Expanding and simplifying, we get:

\(V = -x^3 + x^2\sqrt(x^2 + 216.75)\)

The dimensions that will result in a solid with maximum volume, we need to find the value of x that maximizes the volume V.

We can do this by taking the derivative of V with respect to x, setting it equal to zero, and solving for x:

\(dV/dx = -3x^2 + 2x\sqrt(x^2 + 216.75) + x^2/(2\sqrt (x^2 + 216.75)) = 0\)

Multiplying both sides by \(2\sqrt (x^2 + 216.75)\) to eliminate the denominator, we get:

\(-6x^2\sqrt (x^2 + 216.75) + 4x(x^2 + 216.75) + x^3 = 0\)

Simplifying, we get:

\(x^3 - 6x^2\sqrt (x^2 + 216.75) + 4x(x^2 + 216.75) = 0\)

We can solve this equation numerically using a graphing calculator or computer software.

\(The solution is approximately x = 6.34 centimeters.\)

Substituting x = 6.34 into the expression for y and z, we get:

\(y = z \approx 9.03 centimeters\)

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Answer:

52 square units

Step-by-step explanation:

For this you need the length of CB and the length of DA.

|CB| = √(10²+2²) = 2√26

|DA| = √(10²+2²) = 2√26

area of ABC = base · height / 2 = 2√26 · 2√26 / 2 = 52

The area under the curve of the function from x = 1 to x = 13 is -36 square units for both overestimation and underestimation.

The height of the second rectangle is f(4), the height of the third rectangle is f(7), and the height of the fourth rectangle is f(10). Overestimate using an upper sum: The area under the curve of the function from x = 1 to x = 13 is to be overestimated using an upper sum. An upper sum is the sum of the areas of the rectangles where the height of each rectangle is the maximum value of the function in the interval of the rectangle. The upper sum is given by: `upper sum = f(1)Δx + f(4)Δx + f(7)Δx + f(10)Δx`. The height of the rectangle starting at x = 1 is f(1) = -13 + 14(1) - (1)² = -12. The height of the rectangle starting at x = 4 is f(4) = -13 + 14(4) - (4)² = 3. The height of the rectangle starting at x = 7 is f(7) = -13 + 14(7) - (7)² = -20. The height of the rectangle starting at x = 10 is f(10) = -13 + 14(10) - (10)² = 17. Thus, `upper sum = (-12)(3) + (3)(3) + (-20)(3) + (17)(3) = -36 + 9 - 60 + 51 = -36`. Therefore, the overestimated area under the curve of the function from x = 1 to x = 13 is -36 square units.

Underestimate using a lower sum: The area under the curve of the function from x = 1 to x = 13 is to be underestimated using a lower sum. The minimum value of the function in the interval of the rectangle starting at x = 7 is f(7) = -20. The minimum value of the function in the interval of the rectangle starting at x = 10 is f(10) = 17. Thus, `lower sum = (-12)(3) + (3)(3) + (-20)(3) + (17)(3) = -36 + 9 - 60 + 51 = -36`. Therefore, the underestimated area under the curve of the function from x = 1 to x = 13 is -36 square units.

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