Use your mouse or finger to split the


trapezoid into two triangles and a rectangle.


I ready

The Lagrange Error Bound for P3(x) is |R3(x)| ≤ 0.00012, where f(x) = [tex]e^x[/tex]and x = 0.

To find the Lagrange Error Bound for the third-degree Taylor polynomial, we need to use the formula: |Rn(x)| ≤ (M / (n + 1)) * [tex]|x - a|^{(n+1)[/tex]

where M is an upper bound for [tex]|f^{(n+1)(x)}|[/tex]on the interval [a,x], and Rn(x) is the remainder or error term in the Taylor series.

For the given function f(x) = [tex]e^x[/tex], we have:

f(x) = [tex]e^x[/tex]

f'(x) = [tex]e^x[/tex]

f''(x) = [tex]e^x[/tex]

f'''(x) = [tex]e^x[/tex]

Since[tex]f^{(4)}(x) = e^x[/tex] is also [tex]e^x[/tex], the maximum value of |f^(4)(x)| on the interval [-0.25,0.25] is [tex]e^{0.25[/tex].

Thus, we can set [tex]M = e^{0.25[/tex] and a = 0. Then, using n = 3 (for the third-degree Taylor polynomial), we have:

|R3(x)| ≤ [tex](e^{0.25 / (3 + 1)}) * |x - 0|^4[/tex]

Simplifying, we get:

|R3(x)| ≤ 0.000125 * x⁴

Since x = 0.25 for this problem, we get:

|R3(0.25)| ≤ 0.000125 * 0.25⁴ = 0.00012

Therefore, the Lagrange Error Bound for P3(x) is |R3(x)| ≤ 0.00012, where f(x) =[tex]e^x[/tex] and x = 0. We can use this bound to estimate the accuracy of the third-degree Taylor polynomial approximation for [tex]e^{0.25[/tex].

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1. A psychologist selects 12 boys and 12 girls from each of four Science classes. = Stratified sampling

2. When he made an important announcement, he based his conclusion on 10 000 responses, from 100 000 questionnaires distributed to students= Convenience sampling

3. A biologist surveys all students from each of 15 randomly selected classes = Cluster sampling

4. The game show organizer writes the name of each contestant on a separate card, shuffles the cards, and draws five names= Random sampling

5. Family Planning polls 1 000 men and 1 000 women about their views concerning the use of contraceptives= Stratified sampling

6. A hospital researcher interviews all diabetic patients in each of ten randomly selected hospitals = Cluster sampling

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1a. The period of the motion is the time it takes for the horse to complete one full cycle of motion, and it is given by:

T = 2π/ω.

See attached graph.

1b. The period of the motion is the time it takes for the carousel to complete one full cycle of motion, and it is also given by:

T = 2π/ω.

1a.
let's assume that the motion of the horse can be modeled by a simple harmonic motion. The equation for simple harmonic motion is:

y = A sin(ωt + φ)

where:

y is the displacement from the equilibrium position

A is the amplitude (maximum displacement)

ω is the angular frequency (2π times the frequency)

t is time

φ is the phase angle

Assuming that the horse's motion is in a vertical direction and that the highest point of its motion corresponds to y = 0, we can write the equation as:

y = A sin(ωt)

where A is the amplitude of the motion and ω is the angular frequency.

We can plot this function as a sine wave on a graph, where the horizontal axis represents time and the vertical axis represents displacement. The period of the motion is the time it takes for the horse to complete one full cycle of motion, and it is given by:

T = 2π/ω

To determine when Ivan will get his next opportunity to take a perfect shot, we need to know the period of the horse's motion. Without additional information, it's difficult to estimate the period accurately.


The graph of the carousel equation θ = A cos(ωt) can be labeled as follows:

1b.
The motion of the carousel can also be modeled as a simple harmonic motion, with the equation:

θ = A cos(ωt + φ)

where:

θ is the angular displacement from the equilibrium position

A is the amplitude (maximum angular displacement)

ω is the angular frequency (2π times the frequency)

t is time

φ is the phase angle


The period of the motion is the time it takes for the carousel to complete one full cycle of motion, and it is given by:

T = 2π/ω

To determine when Ivan will get his next opportunity to take a perfect shot, we need to know the period of the carousel's motion. Without additional information, it's difficult to estimate the period accurately.

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The estimated daily cost of increasing production to 42 televisions is $3717. Therefore, the closest answer choice is B) $3919.

To estimate the daily cost of increasing production to 42 televisions, we need to first calculate the marginal cost. The marginal cost is the derivative of the cost function:

[tex]C'(x) = -0.009x^2 + 0.2x + 71[/tex]

We can then evaluate the marginal cost at x=40 to find the cost of producing one additional television:

[tex]C'(40) = -0.009(40)^2 + 0.2(40) + 71 = $33.40[/tex]

This means that the cost of producing one additional television when 40 are already being produced is $33.40. To estimate the daily cost of increasing production to 42 televisions, we can multiply the marginal cost by 2 (since we want to produce 2 additional televisions):

[tex]2*$33.40 = $66.80[/tex]

Finally, we can add this estimated cost to the current cost of producing 40 televisions:

[tex]C(40) = -0.003(40)^3 + 0.1(40)^2 + 71(40) + 540 = $3650[/tex]

$3650 + $66.80 = $3716.80

Rounding to the nearest dollar, the estimated daily cost of increasing production to 42 televisions is $3717. Therefore, the closest answer choice is B) $3919.

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In triangle ABC with a right angle at B, to make angle A greater than 75 degrees, you can choose BC = 1 unit and hypotenuse AC = 3 units.

In a right-angled triangle, the sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. In our case, sin(A) = BC/AC. To make angle A greater than 75 degrees, we need sin(A) > sin(75). Using a calculator, sin(75) ≈ 0.9659. So, we need BC/AC > 0.9659.

Let's take BC = 1 unit, then we need AC > 1/0.9659 ≈ 1.035 units. To keep it simple, we can choose AC = 3 units. Now, sin(A) = 1/3 ≈ 0.3333, and the corresponding angle A is around 19.47 degrees. Note that this is greater than 75 degrees, fulfilling the requirement.

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Answer:

Step-by-step explanation:

Let's start by finding the total weight of all five people:

Total weight = Average weight x Number of people

Total weight = 107.6 x 5

Total weight = 538

We know that Cathy weighs 115 lb, so we can subtract her weight from the total weight to find the total weight of the other four people:

Total weight of other four = Total weight - Cathy's weight

Total weight of other four = 538 - 115

Total weight of other four = 423

To find the average weight of the other four, we can divide the total weight of the other four by the number of people:

Average weight of other four = Total weight of other four / Number of people

Average weight of other four = 423 / 4

Average weight of other four = 105.75 lb

Therefore, the average weight of the other four is 105.75 lb.

The critical value you will use for your 98% confidence interval with a sample size of 32 is 2.33.

When finding a 98% confidence interval for a normally distributed population with a sample size of 32, you will need to use a critical value from the standard normal (z) distribution.

To find the critical value, you can refer to a z-table or use a calculator with statistical functions. For a 98% confidence interval, you will need the z-score that corresponds to the middle 98% of the data, leaving 1% in each tail. This z-score is approximately 2.33.

So, the critical value you will use for your 98% confidence interval with a sample size of 32 is 2.33.

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Answer:

  236 in²

Step-by-step explanation:

You want the surface area of the figure comprised of two cuboids.

The surface area of the figure will be the sum of the total surface area of the purple cuboid, plus the lateral surface area of the yellow cuboid.

  SA = 2(LW +H(L +W)) + Ph

  SA = 2(9·4 +2(9 +4)) +(4·4)(7) = 236 . . . . square inches

The surface area of the composite figure is 236 square inches.

__

Additional comment

You can consider the face on the right side to be equal in area to the area of the purple cuboid that is covered by the yellow one. So, figuring the total area of the purple cuboid effectively includes the area of the face on the right side.

Then the remaining part of the area of the yellow cuboid is the area of the four 7×4 rectangles that are its lateral area.

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The length of the platform is given by the expression -2 + sqrt(3x^2 + 10x) meters.

Let's start by using the formula for the area of a rectangle, which is:

Area = length x width

We are given that the width of the platform is (x+4) meters, so we can write:

Area = length x (x+4)

We are also given that the area of the platform is 3x^2+10x−8, so we can set these two expressions equal to each other and solve for the length:

3x^2+10x−8 = length x (x+4)

Expanding the right side, we get:

3x^2+10x−8 = length x^2 + 4length

Subtracting 4length from both sides, we get:

3x^2+10x−8−4length = length x^2

Rearranging, we get a quadratic equation:

length x^2 + 4length − 3x^2 − 10x + 8 = 0

To solve for length, we can use the quadratic formula:

length = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 4, and c = -3x^2 - 10x + 8. Plugging in these values, we get:

length = (-4 ± sqrt(4^2 - 4(1)(-3x^2 - 10x + 8))) / 2(1)

Simplifying under the square root:

length = (-4 ± sqrt(16 + 12x^2 + 40x - 32)) / 2

length = (-4 ± sqrt(12x^2 + 40x)) / 2

length = (-4 ± 2sqrt(3x^2 + 10x)) / 2

length = -2 ± sqrt(3x^2 + 10x)

Since the length must be positive, we take the positive square root:

length = -2 + sqrt(3x^2 + 10x)

Therefore, the length of the platform is given by the expression -2 + sqrt(3x^2 + 10x) meters.

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La longitude del Puente entre loss punts A y B es de aproximadamente 97.9 metros.

Para calcular la longitud del puente entre los puntos A y B, podemos utilizar el teorema del seno en el triángulo OAB.

Primero,trazamos una línea vertical desde O hasta el segmento AB, creando un triángulo rectángulo OAD. La distancia entre A y O, medida en línea recta, es de 120 m.

Luego, utilizando el ángulo OAB, que mide 48 grados, y el ángulo ABO, que mide 32 minutos (o 32/60 grados), podemos encontrar el tercer ángulo del triángulo OAB aplicando la propiedad de que la suma de los ángulos de un triángulo es 180 grados.

El tercer ángulo del triángulo OAB será: 180 - 48 - (32/60) ≈ 101.467 grados.

Ahora, aplicamos el teorema del seno:

sen(OAB) / AO = sen(ABO) / BO

Despejando BO

BO = (AO * sen(ABO)) / sen(OAB)

Sustituyendo los valores conocidos:

BO = (120 * sen(48)) / sen(101.467) ≈ 120 * 0.7431 / 0.9933 ≈ 89.568 m

Por lo tanto, la longitud del puente que se quiere construir entre los puntos A y B es aproximadamente 89.568 metros.

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Answer:

a = - 5 , b = 1

Step-by-step explanation:

2a = - 2 + 4(a + 3) ← distribute parenthesis

2a = - 2 + 4a + 12 ( subtract 4a from both sides )

- 2a = 10 ( divide both sides by - 2 )

a = - 5

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

- 4b = - 5(3 - b) + 6 ← distribute parenthesis

- 4b = - 15 + 5b + 6 ( subtract 5b from both sides )

- 9b = - 9 ( divide both sides by - 9 )

b = 1

Step-by-step explanation:

2a=6(a+3)

2a=6a+18

2a-6a=18

-4a=18

-4a/-4=18/-4

a=-4.5

Answer:

To make 3 gallons of punch, you need 2 cups of cranberry juice.

We can set up a proportion to find out how much cranberry juice is needed for 1 gallon of punch:

2 cups / 3 gallons = x cups / 1 gallon

To solve for x, we can cross-multiply:

2 cups * 1 gallon = 3 gallons * x cups

2 cups = 3x

x = 2/3 cup

Therefore, you would need 2/3 cup of cranberry juice to make 1 gallon of punch using this recipe.

Considering the ratio, Ginger can make four different smaller necklaces.

The ratio between two amounts a and b is given as follows:

a to b.

Which is also the division of the two amounts.

The ratio for this problem is given as follows:

Pink/White = 30/35

Pink/White = 6/7 -> as 30/6 = 5 and 35/7 = 5.

5 - 1 = 4, hence, considering the ratio, Ginger can make four different smaller necklaces.

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The value of x and y in the right triangle are 11.31 units and 8 units respectively.

The tangential ratio of ∠P and ∠Q are 16 / 12 and 12 / 16 respectively.

A right angle triangle is a triangle that has one of its angles as 90 degrees. The side of a right angle triangle can be found using trigonometric ratios as follows:

tan 45 = opposite / adjacent

tan 45 = 8 / y

cross multiply

y = 8 / tan 45

y = 8  /1

y = 8 units

Therefore,

sin 45 = opposite / hypotenuse

sin 45 = 8 / x

cross multiply

x = 8 / sin 45

x = 11.313816999

x = 11.31 units

Let's find the tangent ratio of ∠p and ∠q.

Hence,

tan ∠P = 16 / 12

tan ∠Q = 12 / 16

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The choir practice this week for 5 1/4 hours.

On Monday, the choir practiced for 3/4 hour.

On Wednesday, they practiced for 1/2 hour more than on Monday, which is 3/4 + 1/2 = 6/8 + 4/8 = 10/8 = 1 1/4 hours.

On Friday, they practiced twice as long as on both Monday and Wednesday combined, which is 2 * (3/4 + 1 1/4) = 2 * 2 = 4 hours.

To find the total practice time for the week, we can add up the times from each day:

3/4 + 1 1/4 + 4 = 5 + 1/4 = 5 1/4 hours.

Therefore, the choir practiced for 5 1/4 hours in total this week.

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The linearization of the function z = x =√y at the point (-2, 4) is L(x, y) = 2 + (1/4)(y-4).

To find the linearization of the function z = x =√y at the point (-2, 4), we need to use the formula for the linearization:

[tex]L(x, y) = f(a, b) + f_x(a, b)(x-a) + f_y(a, b)(y-b)[/tex]

where f(a, b) is the value of the function at the point (a, b), f_x(a, b) is the partial derivative of f with respect to x evaluated at (a, b), f_y(a, b) is the partial derivative of f with respect to y evaluated at (a, b), and (x-a) and (y-b) are the distances from the point (a, b) to the point (x, y).

In this case, we have:
f(x, y) = √y
a = -2
b = 4

So, we need to find the partial derivatives f_x and f_y:

[tex]f_x(x, y) = 0f_y(x, y) = 1/(2√y)[/tex]

evaluated at (a, b):

f_x(-2, 4) = 0
f_y(-2, 4) = 1/(2√4) = 1/4

Now, we can plug in all the values into the linearization formula:

[tex]L(x, y) = f(-2, 4) + f_x(-2, 4)(x-(-2)) + f_y(-2, 4)(y-4)L(x, y) = √4 + 0(x+2) + (1/4)(y-4)L(x, y) = 2 + (1/4)(y-4)[/tex]

Therefore, the linearization of the function z = x =√y at the point (-2, 4) is L(x, y) = 2 + (1/4)(y-4).

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The measure of a central angle of a regular polygon with 7 sides is approximately 51.4 degrees.

For a regular polygon with 7 sides, we can substitute n = 7 into the formula:

central angle = 360 degrees / 7

central angle ≈ 51.4 degrees

A regular polygon is a polygon with equal sides and equal angles. The measure of each interior angle of a regular polygon with n sides is given by the formula:

interior angle = (n-2) x 180 degrees / n

For example, for a regular polygon with 7 sides:

interior angle = (7-2) x 180 degrees / 7

interior angle = 5 x 180 degrees / 7

interior angle ≈ 128.6 degrees

Since a central angle of a regular polygon is an angle formed by two consecutive radii from the center of the polygon, the measure of a central angle is equal to the measure of the exterior angle.

The measure of an exterior angle of a regular polygon with n sides is given by the formula:

exterior angle = 360 degrees / n

For a regular polygon with 7 sides, we can use the formula above to find the measure of each exterior angle:

exterior angle = 360 degrees / 7

exterior angle ≈ 51.4 degrees

Therefore, the measure of a central angle of a regular polygon with 7 sides is approximately 51.4 degrees, rounded to the nearest tenth of a degree as requested.

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In order to find the probability of a student playing on the football team given that they play in the band, we'll use conditional probability.

The formula for conditional probability is P(A|B) = P(A and B) / P(B).

In this case, A represents playing on the football team, and B represents playing in the band.

Given:
P(B) = 0.15 (probability of playing in the band)
P(A and B) = 0.03 (probability of playing in the band and on the football team)

Now we can apply the formula:

P(A|B) = P(A and B) / P(B) = 0.03 / 0.15 = 0.2

So, the probability that a student at Kennedy High School plays on the football team given that they play in the band is 0.2 or 20%.

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The survey randomly selected students nationwide if they traveled outside the country for spring break and a 99% confidence interval which is 753 students.

The formula for a confidence interval for a proportion is:

CI = p ± z*sqrt((p*(1-p))/n)

where p is the sample proportion, n is the sample size, and z is the critical value from the standard normal distribution corresponding to the desired confidence level.

In this case, the confidence interval is given as (0.0994, 0.1406), which means:

p = (0.0994 + 0.1406) / 2 = 0.1200

The critical value for a 99% confidence interval is z = 2.576.

Substituting these values into the formula and solving for n, we get:

0.0206 = 2.576*sqrt((0.12*(1-0.12))/n)

Squaring both sides and solving for n, we get:

n = (2.576² * 0.12 * 0.88) / (0.0206²) = 752.3

Rounding up to the nearest integer, we get:

n = 753

Therefore, the survey included 753 students.

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The measure of angle A is given as follows:

m < A = 53.13º.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

Angle A is opposite to a side of length 4 cm, while the hypotenuse is of 5 cm, hence it's measure is obtained as follows:

sin(A) = 4/5

m < A = arcsin(4/5)

m < A = 53.13º.

We have a right triangle, in which the side length opposite to angle A is BC = 4, while the hypotenuse is CA = 5.

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The length of segment C'D' is given as follows:

C'D' = 2.

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

The length of segment CD is given as follows:

CD = 4. (4 vertical units of difference).

The scale factor is given as follows:

k = 1/2.

Hence the length of segment C'D' is given as follows:

C'D' = 1/2 x 4 = 2.

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The surface area of the cylinder, rounded to the nearest square meter, is: D. 120 square meters

The surface area of a cylinder can be calculated by using the formula expressed as:

SA = 2πr(h + r), where r is the radius and h is the height.

Given the following:

π = 3.14

radius (r) = 2.2 m

height of the cylinder (h) = 6.5 m

Plug in the values:

SA = 2 * 3.14 * 2.2 * (6.5 + 2.2)

SA ≈ 120 square meters (rounded to the nearest square meter)

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Answer:23.4

Step-by-step explanation: 18 divided by 130

The amount of the discount is $23.40.

The problem asks us to find the amount of the discount given a percentage discount on a known price. To do this, we use the formula for calculating a percentage of a number.

To calculate the discount amount, we need to find 18% of the original price, which is $130 per week.

We can start by calculating 18% of $130:

Discount = 0.18 * $130 = $23.40

Therefore, the amount of the discount is $23.40.

the final result will be 3n + 21

what is ditribustion propety?

The Distributive Property is a mathematical property that states that when a single term is multiplied by a sum or difference, the result can be expressed as the sum or difference of the products of the term multiplied by each term inside the parentheses. It is often used to simplify expressions and equations in algebra. 3(x + 2) = 3x + 32 (distributing the 3 over the parentheses) = 3x + 6 (simplifying the products) This property is very useful when dealing with expressions containing variables or unknowns, as it allows us to simplify complex expressions and solve equations more easily.

using distribution propety

3(n + 7)

= (3)(n) + (3)(7)

= 3n + 21

Hence the final result will be 3n + 21

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Answer: The answer is (A

Step-by-step explanation:

The answer isB because A is constant, C is irrelevant, and D is dependent.

Enzo's statement that he can draw an enlarged rectangle that is 16 centimeters by 13 centimeters is correct. To explain this, we need to understand what it means to enlarge a shape.

Enlargement is the process of making a shape bigger or smaller while maintaining its shape and proportions. In other words, if we enlarge a rectangle, we need to make sure that the length and width are increased by the same factor.

In this case, Enzo has specified the new dimensions of the rectangle as 16 centimeters by 13 centimeters. To create an enlarged rectangle with these dimensions, we need to know the scale factor of the enlargement. The scale factor is the ratio of the length of the enlarged shape to the length of the original shape. In this case, we can find the scale factor by dividing the length of the new rectangle (16 centimeters) by the length of the original rectangle.

Let's assume that the original rectangle has a length of 8 centimeters and a width of 6 centimeters. Dividing 16 by 8 gives us a scale factor of 2. This means that we need to multiply the length and width of the original rectangle by 2 to get the dimensions of the enlarged rectangle.

So, the length of the enlarged rectangle will be 8 x 2 = 16 centimeters, and the width will be 6 x 2 = 12 centimeters. However, Enzo has specified that the width of the enlarged rectangle should be 13 centimeters. This means that we need to adjust the scale factor to make the width of the enlarged rectangle 13 centimeters. Dividing 13 by 6 gives us a scale factor of approximately 2.17.

Multiplying the length and width of the original rectangle by this scale factor gives us the new dimensions of the enlarged rectangle. The length will be 8 x 2.17 = 17.36 centimeters (rounded to two decimal places), and the width will be 6 x 2.17 = 13.02 centimeters (rounded to two decimal places). Therefore, Enzo is correct in saying that he can draw an enlarged rectangle that is 16 centimeters by 13 centimeters.

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To find the percent error for the stopwatch's measurement of Stacy's time in her 50-meter freestyle race, we'll use the following formula:
Percent Error = (|(Measured Value - Actual Value)| / Actual Value) * 100

Here, the Measured Value is the stopwatch's time (32.4 seconds), and the Actual Value is the electronic touchpad's time (32.36 seconds).

Step 1: Calculate the absolute difference between the measured and actual values:
|32.4 - 32.36| = 0.04

Step 2: Divide the absolute difference by the actual value:
0.04 / 32.36 = 0.001236

Step 3: Multiply the result by 100 to get the percentage:
0.001236 * 100 = 0.1236%

The percent error for the stopwatch's measurement of Stacy's time in her 50-meter freestyle race is approximately 0.124%.

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The radian measure -1.7 pi is equivalent to -306 degrees.

To find the percent error of the stopwatch's measurement, we need to compare it to the more precise electronic touchpad measurement. The formula for percent error is:

percent error = (|measured value - actual value| / actual value) x 100%

In this case, the measured value is 32.4 seconds, the actual value is 32.36 seconds, and the absolute difference between them is 0.04 seconds. Plugging these values into the formula, we get:

percent error = (|32.4 - 32.36| / 32.36) x 100% = 0.124%

Therefore, the percent error for the stopwatch's measurement is 0.124%. This means that the stopwatch's measurement was very close to the actual value, with an error of only 0.124% of the actual value.

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The given equation on a graph can be described best as C. It will be a line.

The given equation is a linear equation because it has the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the equation can be rewritten as:

y = 3x + 15 - 64

y = 3x - 49

Since it's a linear equation, it will represent a straight line on the graph that can be found by using the equation and some values of x, to find values of y and then plotting them.

In conclusion, the best answer is C. It will be a line.

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The full question is:

An equation is given to be 3x + 15 = 64

What will this be on a graph ?

A. It will be irregular

B. It will be a curve.

C. It will be a line.

D. There is no way to tell.