((2. 88 × 4. 02) + (7. 56 × 3. 13)) ÷ 5. 79 = Answer

Answer:

To calculate the expected value of the game for the player, we need to find the probability of each possible outcome and the corresponding payoff or cost, and then multiply each probability by its payoff or cost, and sum the results. Let's first find the probability of each possible outcome:

- Probability of drawing two green marbles: (6/14) * (5/13) = 0.164

- Probability of not drawing two green marbles: 1 - 0.164 = 0.836

If both marbles are green, the player wins $25, so the payoff is $25. If not, the player must donate $10 to the animal shelter, so the cost is -$10. Therefore, the expected value of the game for the player is:

Expected value = (Probability of winning * Payoff) + (Probability of losing * Cost)

Expected value = (0.164 * $25) + (0.836 * -$10)

Expected value = $4.10 - $8.36

Expected value = -$4.26

The expected value of the game for the player is -$4.26, which means that on average, the player can expect to lose $4.26 per game. Therefore, playing this game is not a good bet for the player.

Given the rectangle's dimensions, its area is 12 cm² and the circle's area is π cm². Thus, the shaded region's area is about 8.57 cm².

The area of the shaded region is equal to the area of the rectangle minus the area of the circle.

The area of the rectangle is given by:

Area of rectangle = length x width = 4 cm x 3 cm = 12 cm²

The area of the circle is given by:

Area of circle = π x radius² = π x (1 cm)² = π cm²

Therefore, the area of the shaded region is:

Area of shaded region = Area of rectangle - Area of circle

Area of shaded region = 12 cm² - π cm²

Area of shaded region ≈ 8.57 cm² (rounded to the nearest hundredth)

Hence, the area of the shaded region is approximately 8.57 cm².

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the missing figure is in the image attached below

Since a 16-ounce bottle of orange juice contains 200 milligrams of vitamin C, we can find the amount of vitamin C in 4 ounces by using a proportion:

16 ounces     200 milligrams

4 ounces       x milligrams

Solving for x, we have:

x = 50 milligrams

So, Yosef drank 50 milligrams of vitamin C.

To find the percent of the daily recommended amount of vitamin C this represents, we can use another proportion:

80 milligrams     100%

50 milligrams      x%

Solving for x, we have:

x = (50/80) * 100 ≈ 62.5%

Therefore, Yosef drank orange juice containing 62.5% of the daily recommended amount of vitamin C.

Joni is not correct because she used the simple interest rate formula, not the compound interest rate formula. She will have $231.53.

A loan or investment's principle amount is the sole amount used to compute simple interest. Any interest that has been earned on interest that has accrued over time is not taken into account by simple interest.

Contrarily, compound interest is a sort of interest that takes into account both the original principal and any interest that has accrued over time. As a result, the interest gained during one period is added to the principle for the following month, where it continues to earn interest.

Joni is not correct, because $230 is just the interest she will earn; she will have $430 total.

The compound interest is given by the formula:

[tex]A = P (1 + r/n)^{(nt)}[/tex]

Substituting the values we have:

[tex]A = 200(1 + 0.05/1)^{(1*3)}\\A = 200(1.05)^3[/tex]

A = 200(1.157625)

A = $231.53

Hence, Joni will have a total balance of $231.53 after 3 years.

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The complete question is:

84 sq ft area does jamie need to cover.

Describe Area?

The region enclosed by an object's form is referred to as the area. The area of the form is the area that the figure or any other two-dimensional geometric shape occupies in a plane.

                        A two-dimensional shape's area, which is expressed in square units, is the total surface area it may occupy. The square metre (m2), a derived measure, serves as the area unit in the SI system. On a sheet of paper, draw a square using a pencil. It has two dimensions. Its Area refers to the area that the form occupies on the paper.

the area of the walkway is:

Area of walkway = length x width = 8 ft x 3.5 ft = 28 sq ft

Next, let's calculate the area of the patio. The patio measures 7 feet from top to bottom and 8 feet across. Therefore, the area of the patio is:

Area of patio = length x width = 7 ft x 8 ft = 56 sq ft

Now, to find the total area that Desiree needs to cover, we just add the area of the walkway and the area of the patio:

Total area = area of walkway + area of patio

Total area = 28 sq ft + 56 sq ft

Total area = 84 sq ft

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Answer: [-4.5  -3.5]

                 [-4     -3]

Step-by-step explanation:

Music and a matrix calculator online, mwah

The expression that makes the equation true= 4 x (2 + 3).

A relation is any subset of a Cartesian product.

As an illustration, a subset of is referred to as a "binary connection from A to B," and more specifically, a "relation on A."

A binary relation from A to B is made up of these ordered pairs (a,b), where the first component is from A and the second component is from B.

Every item in a set X is connected to one item in a different set Y through a connection known as a function (possibly the same set).

A function is only represented by a graph, which is a collection of all ordered pairs (x, f (x)).

Every function, as you can see from these definitions, is a relation from X.

Hence, The expression that makes the equation true=

4 x (2 + 3).

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Answer:

a

Step-by-step explanation:

none

Answer:

The expression that would be used to find the sum of the products in the area model would be:

C) 600 + 60 + 400 + 40 = 1100

we get that the wheel of Kathel's car makes about 146 more revolutions than the wheel of Nguye's lorry to cover a distance of 770 m.

The circumference of a circle is the distance around the outer boundary of the circle. It is the length of the boundary or the "perimeter" of the circle. The circumference is calculated using the formula C = 2πr, where C is the circumference, r is the radius of the circle, and π (pi) is a mathematical constant approximately equal to 3.14159. The circumference is measured in units of length, such as meters or feet.

by the question.

To solve this problem, we need to first find the circumference of each wheel:

[tex]Circumference of Nguyon's lorry wheel = 2πr = 2 x (22/7) x 28 cm = 176[/tex]cm

Circumference of Kathel's car wheel = πd = (22/7) x 42 cm = 132 cm

Next, we can calculate how many revolutions each wheel needs to make to cover a distance of 770 m:

Number of revolutions for Nguyon's lorry wheel = distance ÷ distance covered in one revolution

= 77000 cm ÷ 176 cm ≈ 437.5 revolutions

Number of revolutions for Kathel's car wheel = distance ÷ distance covered in one revolution

= 77000 cm ÷ 132 cm ≈ 583.3 revolutions

Finally, we can find the difference in revolutions between the two wheels:

Difference in revolutions = Number of revolutions for Kathel's car wheel - Number of revolutions for Nguyon's lorry wheel

= 583.3 - 437.5 ≈ 145.8 revolutions

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Answer:

132 seconds aka 2.2 minutes

Step-by-step explanation:

they met at 132 seconds then converted to minutes which is 2.2 minutes

12,24,36,48,60,72,84,96,108,120,132

11,22,33,44,55,66,77,88,99,110,121,132

It will take nearly three years for the car's value to be half of its original price.

The general solution of  function  f^(40)(x) = 0 if f(x)=x−4.

The general solution of a function is an expression that includes all possible solutions to a given differential equation or equation. It usually contains arbitrary constants that are determined by applying initial or boundary conditions.

The general solution allows for a range of solutions, rather than a single specific solution. This allows for flexibility in solving problems, as different initial or boundary conditions can result in different specific solutions.

We first find the general solution of f(x) by integrating the function 40 times.

f(x) = x - 4

f'(x) = 1

f''(x) = 0

f'''(x) = 0

f''''(x) = 0

and so on, until we get to:

f^39(x) = 0

Now, we can take the 40th derivative of the function to get the final answer:

f^(40)(x) = 0

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Answer:

  P'(-2, -2)

Step-by-step explanation:

You want to know the location of P(-2, 4) after it is reflected in y=1.

The image point will be as far below the line y=1 as point P is above the line. The x-coordinate is unchanged.

P is 4 -1 = 3 units above the line y=1.

P' will be 3 units below the line y=1, so its y-coordinate is 1 -3 = -2.

The image point is P'(-2, -2).

__

Additional comment

Reflection in the line y=k is described by the transformation ...

  (x, y) ⇒ (x, 2k-y)

  P(-2, 4) ⇒ P'(-2, 2(1) -4) = P'(-2, -2)

Answer:

The correct responses are:

A) S(10)=S(5) means that there were the same number of students in 2010 as in 2005.

E) S(0) = 2,000 means that there were no students in the year 2000.

B and D are not plausible statements because they imply that there is an inverse relationship between t and S(t), meaning that the number of students decreases as t increases. Also, C is incorrect as it implies that there were fewer students in 2015 than there were in 2010, which contradicts the nature of the situation.

The relationship between A and t is exponential, meaning that as time increases, the number of bacteria grows at an accelerating rate.

An exponential function is a mathematical function of the form:

f(x) = a^x

where "a" is a positive constant called the base, and "x" is the independent variable. The base "a" is usually a number greater than 1, but it can also be a fraction between 0 and 1.

Exponential functions have some key properties that make them useful for modeling many natural phenomena. One of the most important properties is that they exhibit exponential growth or decay, meaning that the rate of change of the function is proportional to the current value of the function.

In the given question,

In the exponential function A=2e^(0.3t), the value of A depends on the value of t. Specifically, A is a function of t, where t is the independent variable and A is the dependent variable. This means that as the value of t changes, the value of A changes as well.

The function describes the growth of some bacteria, where A represents the number of bacteria at time t. The value of t represents the time elapsed since the start of the observation period. The function suggests that the growth rate of the bacteria is proportional to the current number of bacteria, with a growth rate of 0.3 per unit time.

The relationship between A and t is exponential, meaning that as time increases, the number of bacteria grows at an accelerating rate. This relationship can be observed by plotting the function on a graph, where A is plotted on the y-axis and t is plotted on the x-axis. The resulting curve will be a steeply upward-sloping curve that gets steeper and steeper as time goes on.

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From  following equations option B  will produce the hyperbola graph shown in the figure

what is hyperbola ?

A hyperbola is a type of conic section, which is a curve that is formed by the intersection of a plane and a double cone. A hyperbola can also be defined as the set of all points in a plane, the difference of whose distances from two fixed points (called the foci) is a constant.

In the given question,

Based on the shape of the hyperbola shown on the y-axis graph, we can tell that the hyperbola has a vertical transverse axis, which means that its equation must have the form:

(y - k)² / a² - (x - h)² / b² = 1

where (h, k) is the center of the hyperbola, a is the distance from the center to the vertices, and b is the distance from the center to the co-vertices.

Option A is not correct because it produces a hyperbola with a horizontal transverse axis, whereas the given graph has a hyperbola with a vertical transverse axis.

We can eliminate option D since its equation has a transverse axis that is not vertical.

Next, we can eliminate option A since the coefficient of x² is positive, which means that the transverse axis is horizontal.

Option C has a transverse axis that is also horizontal, so we can eliminate it as well.

That leaves us with option B, which has a vertical transverse axis and its equation fits the form we determined earlier. Therefore, the equation Y²/9 - x²/4=1 will produce the hyperbola shown on the y-axis graph

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Convert the rectangular equation to polar form

3x-y+2=0

To convert the rectangular equation 3x - y + 2 = 0 to polar form, we can substitute x = r cos(theta) and y = r sin(theta), where r is the radius and theta is the angle in polar coordinates. This gives:

3(r cos(theta)) - (r sin(theta)) + 2 = 0

Simplifying the equation, we get:

r(3 cos(theta) - sin(theta)) = -2

Dividing both sides by the expression in the parentheses:

r = -2 / (3 cos(theta) - sin(theta))

This is the polar form of the equation.

Convert the rectangular equation to polar form

12.3x-y+2=0

13. xy=4

14. (x+y)-9(x-2)=0 72-36=0

15. y²-8x-16-0 (4-4)(3-4)=0

For the rectangular equation xy = 4, we can convert it to polar form using the substitution x = r cos(theta) and y = r sin(theta), which gives:

r cos(theta) * r sin(theta) = 4

r^2 sin(theta) cos(theta) = 4

Using the identity 2 sin(theta) cos(theta) = sin(2theta), we can simplify the equation to:

r^2 sin(2theta) = 8

r = sqrt(8 / sin(2theta))

This is the polar form of the equation.

For the rectangular equation (x+y) - 9(x-2) = 0, we can simplify it to:

x - 8y + 18 = 0

Then, we can convert it to polar form using the substitution x = r cos(theta) and y = r sin(theta), which gives:

r cos(theta) - 8r sin(theta) + 18 = 0

Simplifying the equation, we get:

r = 18 / (cos(theta) - 8sin(theta))

This is the polar form of the equation.

For the rectangular equation y^2 - 8x - 16 = 0, we can complete the square to get:

y^2 - 8x - 16 = (y - 0)^2 - 16 - 8x

Simplifying the equation, we get:

(y - 0)^2 = 8x + 16

Using the substitution x = r cos(theta) and y = r sin(theta), we get:

r^2 sin^2(theta) = 8r cos(theta) + 16

r^2 sin^2(theta) - 8r cos(theta) - 16 = 0

This equation does not simplify nicely into a standard form of polar equation, but it is still a valid polar form.

16. r = 4 sin θ

17.θ= (π/6)

18. r² = sin 2θ

19. r = 6/(2-3 sin θ)

To convert the polar equation r = 4 sin(theta) to rectangular form, we can use the following trigonometric identities:

sin(theta) = y / r

cos(theta) = x / r

Substituting these into the polar equation, we get:

r = 4 sin(theta)

r = 4 y / r

r^2 = 4 y

x^2 + y^2 = 4 y

This is the rectangular form of the equation.

The equation theta = pi/6 represents a line at an angle of pi/6 radians (30 degrees) from the positive x-axis in the polar coordinate system. In rectangular coordinates, this line has the equation y = x tan(pi/6) = x/sqrt(3).

To convert the polar equation r^2 = sin(2theta) to rectangular form, we can use the following trigonometric identities:

sin(2theta) = 2 sin(theta) cos(theta)

sin(theta) = y / r

cos(theta) = x / r

Substituting these into the polar equation, we get:

r^2 = sin(2theta)

r^2 = 2 sin(theta) cos(theta)

r^2 = 2 (y / r) (x / r)

x^2 + y^2 = 2xy

This is the rectangular form of the equation.

To convert the polar equation r = 6 / (2 - 3 sin(theta)) to rectangular form, we can first substitute sin(theta) = y / r and cos(theta) = x / r, giving:

r = 6 / (2 - 3y / r)

r(2 - 3y / r) = 6

2r - 3y = 6

This is the rectangular form of the equation.

chatgpt

Applying the concept of vertical line test, only graph 1 is qualified to be a function.

An analytical tool for determining if a given relation is a function is the vertical line test. The test is drawing a vertical line somewhere on the relation's graph and determining if it crosses the graph several times.

Every vertical line must cross the graph at exactly one place in order for the relation to be a function. This is due to the fact that there is no ambiguity in the mapping between inputs and outputs, where each input (x-value) corresponds to a certain output (y-value).

On the other hand, the connection is not a function if the vertical line crosses the graph more than once. This is due to the unclear mapping between inputs and outputs and the presence of at least two outputs that correspond to the same input.

Without having to explicitly analyze the relation for all potential inputs, the vertical line test is a helpful technique for rapidly identifying whether a particular relation is a function or not. It is especially beneficial for relational graphs like scatterplots, line graphs, and curves.

Using vertical line test, only graph 1 is a function

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The solution to the inequality 2.4/n < 6 is n > 0.4, and the only value from the given options that satisfies this inequality is 0.5.

What is inequality ?

An inequality is a mathematical statement that compares two values or expressions using inequality symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).

Inequalities express a relationship between two quantities, indicating whether one quantity is less than, greater than, or equal to the other quantity.

We can solve the given inequality as follows:

2.4/n < 6

Multiplying both sides by n (note that n cannot be negative):

2.4 < 6n

Dividing both sides by 6:

0.4 < n

So, any value of n that is greater than 0.4 will be a solution to the inequality.

Out of the given options, only 0.5 is greater than 0.4, so 0.5 is the solution to the inequality.

Therefore, the solution to the inequality 2.4/n < 6 is n > 0.4, and the only value from the given options that satisfies this inequality is 0.5.

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Answer:

14

Step-by-step explanation:

Rewrite the equation: 4*4+3-5

Multiply: 16+3-5

Add: 19-5

Subtract: 14

The value of the missing side length is 9.

The figures in the image are two similar triangle.

Side lengths of smaller triangle are:

x and (10-4)

Side lengths of larger triangle are:

(x+6) and 10

Since the triangle are similar, we take the proportion of the side lengths and solve for x.

x/(10-4) = (x+6)/10

x/6 = (x+6)/10

Cross multiply

x × 10 = 6( x + 6 )

Apply distributive property to eliminate the parenthesis.

x × 10 = 6×x + 6×6

10x = 6x + 36

10x - 6x = 36

4x = 36

x = 36/4

x = 9

Therefore, the value of x is 9.

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All three methods give the same solutions. So, the cost of a chocolate truffle is (4C1 - C2) / 18 and the cost of a caramel turtle candy is (9C1 - 20C2).

An equation is a mathematical statement that shows the equality between two expressions. It consists of an equal sign between two expressions, which are usually separated by variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

Here,

Let x be the cost of a chocolate truffle and y be the cost of a caramel turtle candy. From the given information, we can write the following system of equations:

5x + 2y = C1 (Cost of Chocolate Lovers Bag)

2x + 8y = C2 (Cost of Combusting Caramel Bag)

To solve the system of equations, we can use various strategies. Here are a few:

Method 1: Substitution

We can solve for x or y in one equation and substitute the result into the other equation to eliminate one variable. For example, we can solve for x in the first equation:

5x + 2y = C1

5x = C1 - 2y

x = (C1 - 2y) / 5

Substituting this into the second equation:

2((C1 - 2y) / 5) + 8y = C2

Simplifying and solving for y:

C1/5 - 4y/5 + 8y = C2

y = (5C2 - C1) / 26

Substituting this value of y into the first equation and solving for x:

5x + 2((5C2 - C1) / 26) = C1

x = (3C1 - 10C2) / 65

Therefore, the cost of a chocolate truffle is (3C1 - 10C2) / 65 and the cost of a caramel turtle candy is (5C2 - C1) / 26.

Method 2: Elimination

We can multiply the first equation by 4 and the second equation by -1, and add them to eliminate y:

20x + 8y = 4C1

-2x - 8y = -C2

Adding these equations gives:

18x = 4C1 - C2

x = (4C1 - C2) / 18

Substituting this into the first equation and solving for y:

5((4C1 - C2) / 18) + 2y = C1

y = (9C1 - 20C2) / 36

Therefore, the cost of a chocolate truffle is (4C1 - C2) / 18 and the cost of a caramel turtle candy is (9C1 - 20C2) / 36.

Method 3: Matrix algebra

We can write the system of equations in matrix form:

[5 2] [x] [C1]

[2 8] [y] = [C2]

Using matrix algebra, we can solve for the variables:

[x] [C1] [8 -2] [y]

[y] = [C2] [-2 5 ] [x]

Multiplying the matrices, we get:

[x] [8x - 2y] [C1]

[y] = [-2x + 5y] * [C2]

Solving for x and y:

x = (4C1 - C2) / 18

y = (9C1 - 20C2) / 36

Therefore, the cost of a chocolate truffle is (4C1 - C2) / 18 and the cost of a caramel turtle candy is (9C1 - 20C2) / 36.

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Answer:

270 students walked to school

30% students walked to school

Step-by-step explanation:

270 /900 is 30%

Answer:

Step-by-step explanation:

first mark the 30% line. then divide 900 by 0.3 to get 30% of the students (270)

Answer:

To graph the function f(x) = 2sin(x) - 2 by hand, we can use the following steps:

Step 1: Find the amplitude

The amplitude of the function is the absolute value of the coefficient of the sine function, which is 2 in this case. Therefore, the amplitude is 2.

Step 2: Find the period

The period of the function is given by the formula 2π/b, where b is the coefficient of x in the sine function. In this case, b = 1, so the period is 2π/1 = 2π.

Step 3: Find the midline

The midline is the horizontal line that the graph oscillates around. For the sine function, the midline is the y-value of the function when there is no vertical shift. In this case, the midline is y = -2.

Step 4: Find the y-intercept

The y-intercept is the value of the function when x = 0. Plugging in x = 0, we get f(0) = 2sin(0) - 2 = -2. Therefore, the y-intercept is -2.

Step 5: Sketch the graph

Based on the amplitude, period, midline, and y-intercept we just found, we can sketch the graph of the function as follows:

- The graph oscillates between y = 2 and y = -6, with a midline at y = -2.

- The graph starts at (0, -2), then goes up to (π/2, 0), down to (π, -2), down further to (3π/2, -4), and back up to (2π, -2).

- The graph is symmetric about the midline.

Therefore, the information about the function is:

Amplitude: 2 (The distance from the midline to the maximum or minimum of the graph is 2.)

Period: 2π (The graph completes one full cycle over a horizontal distance of 2π.)

Midline: y = -2 (The horizontal line that the graph oscillates around.)

y-intercept: -2 (The value of the function when x = 0.)

According to the given information, the absolute value is |x - 7/6| = 5/6.

What is an algebraic expression?

A mathematical expression known as an algebraic expression can include variables, integers, and mathematical operations including addition, subtraction, multiplication, and division.

When expressing quantities or values that might change depending on the values given to the expression's variables, algebraic expressions are utilised. Expressions in algebra can include one or more variables and be simple or complex.

Two solutions x=1/2, x=-1/3

|x - 7/6| = 5/6.

We know that the absolute value of (1/2 - 7/6) equals the absolute value of (-1/3 - 7/6) because they are opposites and have the same absolute value. So we need an expression that equals 5/6 when either 1/2 - 7/6 or -1/3 - 7/6 is plugged in for x.

To get an expression that equals 5/6 when 1/2 - 7/6 is plugged in for x, we can subtract 7/6 from 1/2 and take the absolute value of the result:

|1/2 - 7/6| = |-1/6| = 1/6.

To get an expression that equals 5/6 when -1/3 - 7/6 is plugged in for x, we can subtract 7/6 from -1/3 and take the absolute value of the result:

|-1/3 - 7/6| = |-9/6| = 3/2.

Since both expressions have the same absolute value of 5/6, we can use either one as the absolute value expression in the equation. Thus,

|x - 7/6| = 5/6.

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To find the distance traveled by the amoeba, we need to calculate the Euclidean distance between the starting point B3 and the ending point G7.

Using the Pythagorean theorem, we can find the length of the diagonal line connecting these two points:

d = √[(G - B)² + (7 - 3)²] * 2

where G - B represents the horizontal distance between the two points in number of squares.

In this case, G - B = 6 (from B to G there are 6 squares horizontally).

Substituting the values, we get:

d = √[6² + 4²] * 2 = √(36 + 16) * 2 = √52 * 2 ≈ 11.4 mm

Therefore, the amoeba travels approximately 11.4 mm. Rounded to the nearest 10th, the distance is 11.4 ≈ 11.4 mm.

The likelihood of being over 67 inches tall is 0.127978, or 12.8%.

The probability of an event occurring is referred to as probability. We frequently have to make predictions about the future in real life. We may or may not be aware of the outcome of an event.At the point when this happens, we broadcast that there is plausible that the occasion will happen.

In conclusion, probability can be put to great use in business as well as in this rapidly expanding field of artificial intelligence.

By simply dividing the total number of outcomes by the favorable number of possibilities, the probability of an event can be calculated using the probability formula.

5 feet 7 inches equals (5*12 +7) inches, or (60 +7) inches, according to our question.

(67 - 69.1)/(2.65) = -1.136 is the z-score.

The probability of having a height greater than 67 inches is 0.127978, or 12.8%.

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Resistance bands, loop bands, tube bands with handles, and cable machines can be used for single-arm rows

In a single-arm row exercise, a variety of equipment can be used to add resistance and challenge the muscles. Here are some examples of what can be submitted for bands in a single-arm row

Resistance bands: Resistance bands are a popular option for single-arm rows. They come in different colors to indicate the level of resistance and can be easily adjusted to increase or decrease the difficulty. To perform a single-arm row with a resistance band, step on the center of the band with one foot and grasp the other end with one hand

Loop bands: Loop bands are a type of resistance band that is formed into a loop. They can be placed around the wrists or forearms to provide resistance during a single-arm row. To perform a single-arm row with a loop band, loop the band around your hand and hold onto the other end with your other hand.

Tube bands with handles: Tube bands with handles are another option for single-arm rows. These bands have handles on each end, allowing for a more comfortable grip. To perform a single-arm row with a tube band, attach one end of the band to a stationary object and hold onto the other end with one hand.

Cable machines: Cable machines are a piece of gym equipment that can also be used for single-arm rows. To perform a single-arm row on a cable machine, adjust the weight to the desired resistance and attach a handle to the cable.

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Answer:

Step-by-step explanation: add all of them together

The ratios are not the same for all values of x and y, we can conclude that x and y are not proportional.

Ratio and proportion are two mathematical concepts that are closely related.

A ratio is a way of comparing two or more quantities by dividing one quantity by another. It expresses the relative size or magnitude of two quantities. Proportion, on the other hand, refers to the equality of two ratios. It states that two ratios are equal. Proportions can be used to solve problems involving unknown quantities.

To determine whether x and y are proportional, we need to check if the ratio of corresponding values of x and y is always the same.

Let's find the ratio of y to x for each corresponding value:

y/x for x=1: 7/1 = 7

y/x for x=2: 8/2 = 4

y/x for x=3: 9/3 = 3

Since the ratios are not the same for all values of x and y, we can conclude that x and y are not proportional.

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