Each statement can be represented with a fraction and a division expression. Move the correct fraction and division expression to each line.

There are 5 identical pieces cut from 3 feet of rope. The length, in feet, of each piece of rope is____ or ____

There are 2 muffins shared equally by 3 friends. The amount of muffin that each friend gets is ____ or ____


pls answer quick! I will give brainiest to whoever is right

The length of the hypotenuse in the given right-angle triangle is 7.5 feet.

According to Pythagoras' theorem, "the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides." Perpendicular, Base, and Hypotenuse are the names given to the triangle's sides. The hypotenuse is the longest side in this case since it is opposite the angle of 90°.

It is a right-angle triangle.

[tex]c = \sqrt{6^{2} +4^{2} } \\c = \sqrt{36 + 16}\\ c = \sqrt{56}\\ c = 7.48[/tex]which is nearly equal to 7.5

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Complete question:

Area of rectangle = 50 [tex]unit^2[/tex].

Perimeter of rectangle =30 unit.

Area of dilated rectangle = 1250  [tex]unit^2[/tex].

Perimeter of dilated rectangle = 150 unit.

What is dilation?

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. Yet, there is a variation in the shape's size.

Here the given rectangle length l = 10 unit and width = 5 unit.

Now using formulas,

Area of rectangle = lw square unit.

=> A = 10*5 = 50 [tex]unit^2[/tex].

Perimeter of rectangle = 2(l+w) unit

=> P =2(10+5) = 2(15) = 30 unit.

Here scale factor= 5

The dilated rectangle length [tex]l_1[/tex]= 10*5 = 50 unit and

width [tex]w_1 = 5\times5 = 25[/tex] unit

Now area of dilated rectangle [tex]A_1[/tex]= [tex]l_1w_1[/tex] square unit.

=>  [tex]A_1[/tex]= 50*25 = 1250  [tex]unit^2[/tex].

Perimeter of dilated rectangle [tex]P__1[/tex] = 2([tex]l_1+w_1)[/tex] unit.

=>  [tex]P__1[/tex] = = 2(50+25) = 2(75) = 150 unit.

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Ann drinks 125 milliliters of water each hour to stay on track and finish her 1-liter water bottle by the end of the school day.

To solve this problem, we first need to convert the given volume of water from liters to milliliters since milliliters are a more appropriate unit of measurement for the amount of water that Ann drinks each hour.

1 liter = 1000 milliliters

Therefore, Ann drinks 1000 milliliters of water in total for the day.

To find out how many milliliters of water Ann drinks each hour, we can divide the total amount of water by the number of hours she drinks it for.

1000 milliliters / 8 hours = 125 milliliters per hour

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Grand mean of the response variable. In a two-way ANOVA (Analysis of Variance) test, the sum of squares for factor A (also called the "between-groups" sum of squares for factor A) measures the variation in the response variable that can be attributed to the levels of factor A.

Specifically, it measures the sum of the squared differences between the mean of each level of factor A and the grand mean of the response variable (which is the mean of all the observations across all levels of factor A and factor B).

Mathematically, the sum of squares for factor A can be expressed as:

SSA = ∑ni(ȳi.-ȳ..)²

where ni is the sample size of the i-th level of factor A, ȳi. is the mean of the i-th level of factor A, and ȳ.. is the grand mean of the response variable.

In other words, the sum of squares for factor A represents the variation in the response variable that is due to the differences between the means of the levels of factor A, after taking into account the overall mean of the response variable.

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In a two-way ANOVA test, the sum of squares for factor A is based on the sum of the squared differences between the mean for each level of factor A and the overall mean of the data.

This represents the variation in the data that can be attributed to the different levels of factor A.

The sum of squares for factor B is calculated in the same way, but for the levels of factor B instead.

The interaction term in the ANOVA represents the variation that cannot be explained by either factor A or factor B

alone, but is instead due to the combination of the two factors.

Overall, the ANOVA test allows us to determine if there are significant differences between the means of different

groups, and if these differences are due to the factors being tested or random chance.

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Answer:

Plot (-3, -6). From this point, go up 4 units, then right 5 units, to (2, -2). Plot (2, -2), and then draw a line that goes through these two points.

The values of the exponential function are calculated below and as x increases, the exponential function increases.

In the table of function given, we can calculate the value of f(x) as it relates to x.

The given exponential function is ;

f(x) = 2ˣ

Substituting the values;

f(-4) = 2⁻⁴ = 1/2⁴ = 1/16

f(-3) = 2⁻³ = 1/2³ = 1/8

f(-2) = 2⁻² = 1/2² = 1/4

f(-1) = 2⁻¹ = 1/2

f(0) = 2⁻⁰ = 1/2⁰ = 1

As the value of x increases, the exponential function increases.

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The average discount that is obtained by spinning the spinner is 17.7%.

Let, the probability of landing on an even number is denoted by P(E) and the probability of landing on an odd number is denoted by P(O).

We have that the pointer lands on an even number 135 times out of 250 spins.

So, the probability that is of landing on an even number is:

P(E) = Number of times the pointer lands on an even number / Total number of spins

P(E) = 135 / 250

Since, we have the sum of probabilities of all possible outcomes must be 1, we can find the probability of landing on an odd number as follows:

P(O) = 1 - P(E)

P(O) = 1 - (135 / 250)

Now, we know that even numbers get 20% off, and odd numbers get 15% off.

We find the average discount considering these probabilities:

Average Discount = (P(E) * 20%) + (P(O) * 15%)

Average Discount = (135 / 250) * 20% + [1 - (135 / 250)] * 15%

Now, let's perform the calculations:

Average Discount = (135 / 250) * 0.20 + [1 - (135 / 250)] * 0.15

Average Discount = 0.108 + (1 - 0.54) * 0.15

Average Discount = 0.108 + 0.46 * 0.15

Average Discount = 0.108 + 0.069

Average Discount = 0.177

So, the average discount that is obtained by spinning the spinner is 17.7%.

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complete question:

A clothing store has each customer spin this spinner to reveal a discount. Even numbers get 20% off and odd numbers get 15% off. The pointer lands on an even number 135 times out of 250 spins. find the average discount obtained by spinning the spinner?

The surface area of cylinder M is approximately 184.85 square feet, and the surface area of cylinder N is approximately 401.92 square feet.

Let r_N and h_N be the radius and height of cylinder N, and r_M and h_M be the radius and height of cylinder M. We are given that the radius of cylinder N is equal to its height (rN = hN), and the ratio of the height of cylinder N to the height of cylinder M is 5 : 3.

So, we can write:

hN = rN

hN / hM = 5 / 3

The surface area formulas for cylinders M and N:

Surface Area (M) = 2πr_MhM + 2πr_M^2

Surface Area (N) = 2πrNhN + 2πrN^2

If Surface Area (N) = Surface Area (M) + 256

∴ 2πrNhN + 2πrN^2 = 2πrMhM + 2πrM^2 + 256

Combine like terms:

4πrN^2 = 2πrMhM + 2πrM^2 + 256

Divide both sides by 2π:

2rN^2 = rMhM + rM^2 + 128/π

Since hN = rN, we can write:

hM = (3/5)rN

Now substitute hM into equation

2rN^2 = rM((3/5)rN) + rM^2 + 128/π

2rN^2 = (3/5)rN x ((3/5)rN) + ((3/5)rN)^2 + 128/π

= 2rN^2 = (9/25)rN^2 + (9/25)rN^2 + 128/π

= 2rN^2 = (18/25)rN^2 + 128/π

rN = 5.64, hN = 5.64,

rM = 5.64 x (3/5) = 3.38

rM = 3.38.

let's calculate the surface areas:

Surface Area (M) = 2π(3.38)(3.38) + 2π(3.38)^2 ≈ 71.15 + 113.70 ≈ 184.85 square feet

Surface Area (N) = 2π(5.64)(5.64) + 2π(5.64)^2 ≈ 200.96 + 200.96 ≈ 401.92 square feet

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The probability that a randomly selected bicyclist who tests positive for steroids actually uses steroids is 0.763 (rounded to three decimal places).

We can use Bayes' theorem to calculate the probability that a randomly selected bicyclist who tests positive for steroids actually uses steroids. Let A be the event that a randomly selected bicyclist uses steroids, and B be the event that a randomly selected bicyclist tests positive for steroids. Then, we want to find P(A|B), the probability that a bicyclist uses steroids given that they test positive for steroids:

P(A|B) = P(B|A) * P(A) / P(B)

where P(B|A) is the probability of testing positive given that the bicyclist uses steroids, P(A) is the prior probability of a bicyclist using steroids, and P(B) is the probability of testing positive for steroids.

We are given that P(A) = 0.08, P(B|A) = 0.94, and P(B|not A) = 0.09. We can calculate P(B) using the law of total probability:

P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)

= 0.94 * 0.08 + 0.09 * 0.92

= 0.0976

where P(not A) = 1 - P(A) = 0.92.

Substituting the values we have:

P(A|B) = 0.94 * 0.08 / 0.0976

= 0.763

Therefore, the probability that a randomly selected bicyclist who tests positive for steroids actually uses steroids is 0.763 (rounded to three decimal places).

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The location of point P within line segment AB is (8.333, - 6.667).

Herein we find the a line segment whose endpoints are A(x, y) = (10.2, - 6) and B(x, y) = (4.6, - 8), in which we must locate the point P. This can be done by following line segment AB:

P(x, y) = A(x, y) + (2 / 6) · [B(x, y) - A(x, y)]

P(x, y) = (10.2, - 6) + (2 / 6) · [(4.6, - 8) - (10.2, - 6)]

P(x, y) = (10.2, - 6) + (1 / 3) · (- 5.6, - 2)

P(x, y) = (10.2, - 6) + (- 1.867, - 0.667)

P(x, y) = (8.333, - 6.667)

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As the probability of flooding any given year is 0.05, the probability of not flooding in the next year is 0.95 or 95%.

The probability of flooding in a region once every 20 years means that the probability of flooding any given year is 1/20 or 0.05.

Given that the probability of flooding in any one year is greater than zero, we know that the probability of not flooding is less than 1.

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All answers that describe the quadrilateral are parallelogram and rhombus.

In the diagram provided as seen from online sources, the lines, BO=OD and this equals x. Next, SO=OC which equals s. Since the diagonals bisect each other, we can refer to this as a parallelogram.

Next, angle ABO equals angle ADO and since the opposite sides are parallel and equal, we can also refer to the quadrilateral as a rhombus.

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In 2016, the total number of cars produced in the world was 72 million (rounded to the nearest whole number) by forming linear equation.

In 2011, the total number of cars produced in the world was 59.9 million.

In 2016, the total number of cars produced in the world was 21% greater than the total number produced in 2011.

Let us say in 2016 the total number of cars produced in the world was N million.

Therefore, by expressing the given problem in a linear equation we get,

Total number produced in 2016, N = 59.9 + (21% of 59.9 )     in millions

⇒ N = 59.9 + [tex][ \frac{21}{100} ] 59.9[/tex]     ( in millions )

= 59.9 + 12.579    ( in millions )

= 72.479  ( in millions )

= 72 millions ( rounded to the nearest whole number)

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Answer:

[tex].28(22) + 3 = 9.16[/tex]

The predicted width of a foot with a length of 22 centimeters is 9.16 centimeters.

Answer:

10

Step-by-step explanation:

Answer:

Y= (x+4)(x+4)-21

Step-by-step explanation:

If you are factoring It out:

Y=-2x^2+8x-5 is the same as Y= (x+4)(x+4)-21

Let me know if it is incorrect!

-a friendly 8th grader

The composite function g(h(8)) when evaluated is 94.

From the question, we have the following parameters that can be used in our computation:

g(a) = 4a - 2

h(a) = 3a

To find g(h(8)), we need to first evaluate h(8), and then plug that result into g(a) and simplify.

h(a) is defined as 3a, so h(8) = 3(8) = 24.

Now we can plug in 24 for a in g(a) and simplify:

g(a) = 4a - 2

g(h(8)) = g(24) = 4(24) - 2 = 94

Therefore, g(h(8)) = 94.

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To calculate the distance traveled by an object by first calculating when it is stopped, you need to follow these steps:
1. Identify the terms

2. Use the given information

3. Determine when the object is stopped

4. Calculate the distance traveled

Identify the terms:

For this question, we are focusing on distance, velocity, time, and acceleration. The object is stopped when its velocity is zero.
Use the given information:

Collect any given values such as initial velocity, final velocity, time, and acceleration.
Determine when the object is stopped:

To find out when the object is stopped, you'll need to use the equation v = u + at, where v is final velocity (0 m/s when stopped), u is initial velocity, a is acceleration, and t is time.

Solve for t (time) when the object is stopped: t = (v - u) / a.
Calculate the distance traveled:

Now that you have the time when the object is stopped, use one of the equations of motion to find the distance traveled.

We can use the equation s = ut + 0.5at²,

where s is the distance, u is initial velocity, t is the time when the object is stopped, and a is acceleration.
By following these steps and using the provided terms, you'll be able to calculate the distance traveled by an object by first calculating when it is stopped.

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Answer: Let the side length of the square rug be x, and the dimensions of the rectangular rug be l and w.

In the first arrangement, the three rugs are arranged side by side, with the rectangular rugs aligned vertically and the square rug aligned horizontally. The length of this arrangement is l + 2x, and the width is w. We know that the length is 3 times the width, so we can write:

l + 2x = 3w

In the second arrangement, the two rectangular rugs are arranged side by side, with the square rug placed on top. The length of this arrangement is l, and the width is w + x. We know that the length is twice the width, so we can write:

l = 2(w + x)

We now have two equations with two unknowns, l and w:

l + 2x = 3w

l = 2(w + x)

Substituting the second equation into the first, we get:

2(w + x) + 2x = 3w

4x = w

Substituting this value of w into the second equation, we get:

l = 2(4x) = 8x

So the dimensions of the rectangular rug are 4x by x, and the dimensions of the square rug are x by x.

To find the value of x, we use the measurements given in the diagram:

l + 2x = 60

l = 36

Substituting into the equation l = 2(w + x), we get:

36 = 2(4x + x)

36 = 10x

x = 3.6

So the side length of the square rug is 3.6 feet.

Step-by-step explanation:

The total area of the given figure is 85.2m² respectively.

The quantity of unit squares that cover a closed figure's surface is its area.

Square units like cm² and m² are used to measure area.

A shape's area is a two-dimensional measurement.

The space inside the perimeter or limit of a closed shape is referred to as the "area".

Area of rectangle one:

= l*b

= 4*11.4

= 45.6m²

Area of rectangle second:

= l*b

= 4*8.4

= 33.6m²

Area of the triangle:
= 1/2*b*h

= 1/2*4*(11.4-8.4)

= 1/2*4*3

= 2*3

= 6m²

Total area of the figure: 45.6 + 33.6 + 6 = 85.2m²

Therefore, the total area of the given figure is 85.2m² respectively.

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The new vertices of the triangle after the translation are A'(-3, 7), B(-2, 0), and C(1, 7), which form the resultant matrix:

|-3 -2 1 |

| 7 0 7 |

| 1 1 1 |

In mathematics, a translation refers to a geometric transformation that moves every point in a figure or a space by the same distance in a given direction. In other words, it involves sliding a figure or a point to a new location without changing its size, shape, or orientation.

To translate the triangle by a vector (x, y), we use the following transformation matrix:

|1 0 x|

|0 1 y|

|0 0 1|

For the given triangle with vertices at A(-1, 3), B(0, -4), and C(3, 3), let's assume we want to translate it by a vector (−2, 4). Then the transformation matrix for translation is:

|1 0 -2|

|0 1 4 |

|0 0 1 |

To apply this transformation matrix to each vertex of the triangle, we represent the vertices as column vectors and multiply them by the matrix:

| -1 | | 1 0 -2 | | -3 |

| 3 | -> | 0 1 4 | = | 7 |

| 1 | | 0 0 1 | | 1 |

| 0 | | 1 0 -2 | | -2 |

| -4 | -> | 0 1 4 | = | 0 |

| 1 | | 0 0 1 | | 1 |

| 3 | | 1 0 -2 | | 1 |

| 3 | -> | 0 1 4 | = | 7 |

| 1 | | 0 0 1 | | 1 |

So, the new vertices of the triangle after the translation are A'(-3, 7), B(-2, 0), and C(1, 7), which form the resultant matrix:

|-3 -2 1 |

| 7 0 7 |

| 1 1 1 |

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Cash paid for interest during 2014 was $12,750. Based on the provided Phoenix Corp. information, the question requires you to calculate the cash paid for interest throughout the 2014 calendar year.

Also provided are the amounts for the year's interest expenditure and the balance of interest payable as of December 31, 2013 and 2014.

These are the formulas that can be used to determine the cash paid in interest in 2014:

Interest paid in 2014 minus any increases in interest due equals the cash paid in interest.

The difference between the balance of interest payable as of December 31, 2014, and as of December 31, 2013, can be used to compute the increase in interest payable:

Interest payable at December 31, 2014 minus interest payable at December 31, 2013 equals $6,200 minus $5,700, which equals $500 in

additional interest.

This signifies that the corporation incurred more interest expense than it paid during the year Since the balance of interest payable increased from 2013 to 2014, the corporation incurred more interest expense than it paid in that period. As a result, the money used to pay interest in 2014 is:

Interest paid in 2014 plus the increase in interest due is $12,250 plus $500.= $12,750

Thus, $12,750 is the correct response (D).

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A blocked design compares different independent variable levels by using homogeneous groups of experimental units.

In this type of experimental design, subjects are divided into homogeneous groups, or blocks, based on similar characteristics or traits. These blocks help to control or account for potential confounding variables that may affect the outcome of the experiment.

By grouping subjects into blocks, researchers can reduce the variability within each group and increase the accuracy of the experimental results. This allows for a more precise comparison of the effects of different levels of the independent variable on the dependent variable. Blocked designs are particularly useful when there are natural groupings within the experimental units or when the variability between units is high.

In summary, a blocked design is a powerful experimental tool that can help researchers account for potential confounding factors and reduce variability among experimental units. By doing so, it enables the accurate comparison of different levels of the independent variable, ultimately leading to more reliable and valid results.

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The height of the cone is approximately 1.5 cm.

Both a cone and a cylinder have circular bottoms and are three-dimensional shapes. The lateral surfaces of the two shapes differ most noticeably from one another. A cone has a lateral surface that tapers from a point at the apex to a circular base, whereas a cylinder has a curved lateral surface that is parallel to its base. The volume of a cylinder is calculated using the formula V = πr²h, where r is the radius of the base and h is the height, whereas the volume of a cone is calculated using V = (1/3)πr²h.

The volume of the cone is given as:

V = (1/3)πr²h

Rearranging the equation to isolate h we get:

3V = πr²h

h = (3V)/(πr²)

Now, for  volume

of 48 cm³ and a base with a radius of 4 cm we have:

h = (3(48))/(π(4)²)

h ≈ 1.5 cm

Hence, the height of the cone is approximately 1.5 cm.

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The vertical component of the initial velocity will basically decide where the vertices will be. that is how the initial velocity is related to the vertex of the parabola.

A parabola is a symmetrical curve that is formed by the intersection of a plane and a cone, where the plane is parallel to one of the cone's generating lines. The shape of a parabola is similar to that of a U-shaped curve, but with a sharper curve near the bottom of the U.

The parabola has several important properties, including a focus and a directrix. The focus is a point on the axis of symmetry of the parabola that is equidistant from every point on the curve. The directrix is a line that is perpendicular to the axis of symmetry and is equidistant from every point on the curve.

The equation of a parabola in standard form is y = ax² + bx + c, where "a" determines the direction and shape of the parabola, "b" determines the horizontal shift of the parabola, and "c" determines the vertical shift of the parabola.

The initial velocity will have two component basically, a horizontal component and a vertical component. The vertical component will decide how high the object will go, or in other words the vertical component of the velocity will decide the position of the vertex of the parabolis path which the object is going to follow.

When the vertical component of the velocity becomes 0, the object will be at it's maximum height (i.e the object will be at the vertex of the parabola)

The vertical component of the initial velocity will basically decide where the verties will be. that is how the initial velocity is related to the vertex of the parabola.

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Answer:

To calculate how many standard deviations away from the mean an ACT score of 31 is, we need to use the formula:

z = (x - μ) / σ

Where:

x = ACT score of 31

μ = mean of ACT scores (28)

σ = standard deviation of ACT scores (2)

z = number of standard deviations away from the mean

Substituting the values, we get:

z = (31 - 28) / 2

z = 1.5

Therefore, an ACT score of 31 is 1.5 standard deviations away from the mean.

The second time that d = 4 is approximately 2.275 seconds after the pendulum starts swinging forward from its vertical position at rest.

What is the sinusoidal function?

A sinusoidal function is a mathematical function that describes a repetitive oscillation that resembles a sine or cosine wave. It can be expressed in the general form:

f(x) = A sin (Bx + C) + D

We can use the general form of a sinusoidal function to model the horizontal distance "d" of the tip of the pendulum from its vertical position at rest:

d = A sin(ωt + φ) + C

where:

A = amplitude (maximum displacement) = 7.5 inches

ω = angular frequency = (2π)/T, where T is the period = 3.1 seconds

φ = phase shift (initial horizontal displacement) = 0 (since the pendulum is at rest at t=0)

C = vertical displacement = 0 (since the pendulum is at rest at its vertical position)

Plugging in the given values, we get:

d = 7.5 sin((2π/3.1)t)

Now we can use this equation to answer the given questions:

Determine the value of d when t = 3.1 s:

We simply plug in t = 3.1 into the equation:

d = 7.5 sin((2π/3.1)(3.1))

d = 7.5 sin(2π)

d = 0 inches

Therefore, when t = 3.1 seconds, the horizontal distance of the tip of the pendulum from its vertical position is 0 inches.

Approximate the value of t when d = 4 for the second time:

To find when d = 4 for the second time, we need to find the two values of t for which the sinusoidal function equals 4. We can use the fact that the sine function repeats itself every 2π radians to solve this problem.

First, we find the period of the sinusoidal function:

T = 2π/ω = 2π/(2π/3.1) = 3.1 seconds

Next, we find the time it takes for the function to complete half a cycle, or π radians:

t1 = (π/ω) + kT, where k is an integer

t1 = (π/(2π/3.1)) + k(3.1)

t1 = (3.1/2) + 3.1k

We want to find the second time that d = 4, so we need to find the smallest integer value of k for which t2 > t1, where t2 is the time when d = 4 for the second time.

t2 = (3π/ω) + kT

t2 = (3π/(2π/3.1)) + k(3.1)

t2 = (9.3/2) + 3.1k

We want to find the smallest integer value of k such that t2 > t1 and d = 4:

7.5 sin((2π/3.1)t1) = 4

7.5 sin((2π/3.1)t2) = 4

calculating

t1 ≈ 0.604 s

t2 ≈ 2.275 s

Therefore, the second time that d = 4 is approximately 2.275 seconds after the pendulum starts swinging forward from its vertical position at rest.

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The number of people that prefer mustard is 900 and the graphical representation of a datasets are box plots & circle graphs

The histogram is not given and the data represented on the histogram are not properly presented

This means that the histogram cannot be interpreted

Here, we have

Ketchup = 63

Mustard = 27

Chili = 60

So, we have

Mustard = 27/(63 + 27 + 60) * 5000

Evaluate

Mustard = 900

This means that 900 people prefer mustard

Given that

Data = Milligrams of Vitamin C from 100 different gummy vitamins sold

This data can be represented using a box plot because the five-summary data can be easily identified from the dataset

From the five-summary, the median can be derived

In this case, the graph to use is a circle graph

This is so because the circle graph would show the proportion of the student's preferences

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The second term (20(S + J)) denotes the total number of field goals they both scored in the final 20 minutes.

An expression is a grouping of figures, symbols, and algebra (such as addition, reduction, multiply, and division) that expresses a value. Variables, that are symbols for unknowable values, are symbols that can be included in expressions. The statement can be evaluated to give a specific value after the contents of the variables are assigned. An expression using a variable x, for instance, is 3x + 5. When we give x a number of 2, the expression is evaluated to: 3(2) + 5 = 6 + 5 = 11 . As a result, the expression's value at x = 2 is 11.

given

a. Assume that "S" represents the number of field goals Suzy scores each minute and "J" represents the number of field goals Joshua scores each minute.

The calculation for the total number of field goals Suzy and Joshua score in their 30-minute workout is as follows:

[tex]Field goals total = (9 + 10 S) + (20 (S + J)[/tex]

The first term (9 + 10S) denotes Suzy's total number of field goals in the first 10 minutes, while the second term (20(S + J)) denotes the total number of field goals they both scored in the final 20 minutes.

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Answer:

it's the first one. I

n my thinking