The height, h, in feet of a ball suspended from a spring as a function of time, t, in seconds can be modeled by the equation h = 3 sine (StartFraction pi Over 2 EndFraction (t + 2)) + 5. Which of the following is the graph of this equation?
On a coordinate plane, a curve crosses the y-axis at (0, 5). It increases to (2, 8), and then decreases to (6, 2).
On a coordinate plane, a curve crosses the y-axis at (0, 8). It decreases to (4, 2), and then increases to (8, 8).
On a coordinate plane, a curve crosses the y-axis at (0, 5). It increases to (1, 8), and then decreases to (3, 2).
On a coordinate plane, a curve crosses the y-axis at (0, 5). It decreases to (2, 1), and then increases to (3, 8).

According to the given information, Mack should make 4 necklaces and 8 wristbands to maximize his profit.

What are linear programming problems?

LPP stands for Linear Programming Problems. Linear programming is a mathematical optimization technique used to maximize or minimize a linear objective function subject to a set of linear constraints. An LPP involves identifying a set of decision variables, an objective function that depends linearly on these variables, and a set of constraints that specify linear relationships between the variables. The objective is to find the values of the decision variables that optimize the objective function while satisfying all the constraints.

To solve this problem, we need to use a system of linear inequalities to represent all the constraints. Let's start by defining the variables:

x = number of necklaces

y = number of wristbands

Now we can write the constraints:

Time constraint: Mack has 360 minutes to make the necklaces and wristbands.

40x + 25y ≤ 360

Production constraint: Mack wants to make no more than 12 items.

x + y ≤ 12

Non-negative constraint: Mack cannot make a negative number of necklaces or wristbands.

x ≥ 0, y ≥ 0

To maximize Mack's profit, we need to define the objective function as the total profit:

P = 3x + 2y

Now we can graph these constraints and find the feasible region:

40x + 25y ≤ 360

x + y ≤ 12

x ≥ 0, y ≥ 0

As shown in attachment 1.

The feasible region is the shaded polygon bounded by the lines: x=0, y=0, x + y ≤ 12, and 40x+25y=360.

To find the optimal solution, we need to evaluate the objective function at each corner point of the feasible region:

Corner point A: (0,0)

P = 3(0) + 2(0) = $0

Corner point B: (0,12)

P = 3(0) + 2(12) = $24

Corner point C: (4,8)

P = 3(4) + 2(8) = $28

Corner point D: (9,0)

P = 3(9) + 2(0) = $27

The maximum profit is $28, which occurs when Mack makes 4necklaces and 8 wristbands. Therefore, Mack should make 4 necklaces and 8 wristbands to maximize his profit.

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The area of the rectangle is increasing at a rate of 27,900,000 meters³ per year when the width of the region is 450 meters.

The inner-city revitalization region is a rectangle that is twice as long as it is wide. At a time when the area is 450 meters wide, the width of the region is increasing at a rate of 31 meters per year. The aim is to find out how quickly the area is changing at this point in time. The area of the rectangle is given by the formula,

Area = length × width

Given that the width of the rectangle is increasing at a rate of 31 meters per year. Let's say the width of the rectangle is w meters, and the rate of change in width is dw/dt meters per year. Then, we can say, dw/dt = 31 meters per year

Width of the rectangle is w meters

Length of the rectangle is twice the width, or 2w meters

Area of the rectangle is given by the formula, A = lw= 2w × w= 2w²

Now, we need to find dA/dt, the rate at which the area of the rectangle is changing with respect to time (t).We can find it using the formula,

dA/dt = dA/dw × dw/dt

dA/dw = 4w (differentiate 2w² with respect to w)

dw/dt = 31 meters per yeard

A/dt = dA/dw × dw/dt= 4w × 31= 124w meters² per year

From the given information, the width of the rectangle is 450 meters wide. So, the width is w = 450 meters.

dA/dt = 124w meters² per year

= 124 × 450 meters² per year

= 27,900,000 meters³ per year

Which is the increasing rate of the rectangle.

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Estimate less than the actual answer are 9.75 (less than 10) and 9.55 (less than 10). Estimate more than the actual answer are 38.315 (more than 38) and 8.4(more than 8).

Estimate, a near enough approximation of the true value. To make arithmetic simpler and more understandable, many assumptions are made.

Estimate is less than actual answer :

6.35 + 3.4 = 9.75

2.3 * 4.15 = 9.545 (≈ 9.55)

Estimate is more than actual answer :

7.9 * 4.85 = 38.315

3.6 + 4.8 = 8.4

So here, Estimate less than the actual answer are 9.75 (less than 10) and 9.55 (less than 10). Estimate more than the actual answer are 38.315 (more than 38) and 8.4(more than 8).

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Answer: The answer is 1.8 or 1.83 repeating

Step-by-step explanation: When you do 44 divided by 24 (2 years) it gives you how much she needs to pay per month.

Answer:

Angela pays $1.83 for each magazine.

Step-by-step explanation:

Considering that there are 12 months in 1 year, there would be 12 * 2 = 24 months in 2 years. If she gets one magazine per month, she would get 24 magazines.

She would be paying $44 / 24 magazines = 11/6 ≈ 1.83.

So, she is paying about $1.83 for each magazine.

The length on drawing​ with the given scale is 14.15 cm.

Using the given scale of 1cm to 2m, we can set up the following proportion to find the length on the drawing:

1 cm : 2 m = x cm : 28.3 m

where x is the length on the drawing that we want to find.

To solve for x, we can cross-multiply and simplify:

1 cm * 28.3 m = 2 m * x cm

Evaluate the products and remove the units

28.3 = 2x

Divide both sides by 2 to solve for x

x = 28.3 / 2

Evaluate

x = 14.15

Therefore, the length on the drawing is 14.15 cm.

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Erica can make a maximum of 5 hamburger patties with the amount of meat she has.

In scientific and mathematical computations, unit conversions are crucial because they guarantee that data are stated in the proper units, enabling consistency and correctness. To combine or compare numbers and to understand the findings meaningfully, values must be converted to a standard unit of measurement. Calculation mistakes and erroneous conclusions can result from improper unit conversion.

Given that, a hamburger patty weighs about 6 ounces before it is cooked.

Thus,

2.2 pounds = 35.2 ounces (1 pound = 16 ounces)

35.2 ounces / 6 ounces per patty = 5.87

Erica can make a maximum of 5 hamburger patties with the amount of meat she has.

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Answer: in the following order:
6

0

-2

0

6

Step-by-step explanation:

Just need to evaluate the function for each value of X
for x=1  y=2(1-3)^2-2= 6

for x=2  y=2(2-3)^2-2= 0

for x=3  y=2(3-3)^2-2= - 2

for x=4  y=2(4-3)^2-2= 0

for x=5  y=2(5-3)^2-2= 6

For the given inequality x < -7 we draw a straight line at the point -7. The inequality is not strict, hence the line is dotted.

A mathematical statement called an inequality compares two numbers or expressions, typically by employing a symbol. Inequalities show that two quantities are not equal and that one is more than or less than the other.

Number lines can be used to visualise inequality conditions. Depending on whether the endpoint is part of the solution set or not, numbers that meet the inequality are shaded in or denoted by an open or closed circle. A number line would, for instance, show the inequality x > 2 with an open circle at 2 and shading to the right to show all values higher than 2.

In many areas of mathematics as well as in other disciplines like economics and social sciences, inequality is used.

For the given inequality x < -7 we draw a straight line at the point -7.

The inequality is not strict, hence the line is dotted.

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Therefore , the solution of the given problem of unitary method comes out to be  for each number of t, we can plot the points corresponding to the equation V(t) = 5000 + 1250t .

To accomplish the task, one may use this generally accepted ease, preexisting variables, as well as any significant components from the original Diocesan customizable query. If so, there might be an opportunity to interact with the item once more. Otherwise, every significant factor that affects how algorithmic evidence behaves will be gone.

Here,

=> V(t) = 5000 + 1250t

where V(t) represents the amount of water in the pool at moment t (in hours)

t equals time (in hours)

The pool initially has 5000 gallons of water in it, so we add that to the 1250 t of water introduced by the hose.

We can use the time period as the x-axis (horizontal axis) and the amount of water as the y-axis to graph this equation. (vertical axis).

For instance, we can select the water volume interval from 0 to 20,000 gallons and the time interval from 0 to 16 hours (when the pool is full).

Then, for each number of t, we can plot the points corresponding to the equation V(t) = 5000 + 1250t and connect them with a line in order to get the image.

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The maximum amοunt οf prοfit the cοmpany can make is $543

Prοfit is the mοney yοu have left after paying fοr business expenses. There are three main types οf prοfit: grοss prοfit, οperating and net prοfit.

Grοss prοfit is biggest. It shοws what mοney was left after paying fοr the gοοds and services sοld. Operating prοfit is next. It shοws what's left after alsο paying οperating cοsts such as rent, electricity, phοnes and in sοme cases staff.

Net prοfit cοmes last. It shοws what yοu made after deducting all cοsts and tax. Yοu get tο hοld οntο net prοfit.

Let y represent the amοunt οf prοfit and x represent the selling price.

The relatiοnship between x and y is:

y = -4x² + 141x – 703

The maximum prοfit is at dy/dx = 0, hence:

dy/dx = -8x + 141

-8x + 141 = 0

8x = 141

x = 17.625

The maximum prοfit is:

y = -4(17.625)² + 141(17.625) – 703 = 543

The maximum amοunt οf prοfit the cοmpany can make is $543

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(A) A 95% confidence interval estimate for the percentage of all voters who believe competence is more important than character is (0.538, 0.602).

(B) This is due to the interval's lower bound's value of 0.538, which is higher than 0.5.

(C) In this instance, 95% confidence indicates that if the sampling procedure were repeated numerous times and a 95% confidence interval estimate was calculated for each sample

(A) Using the method below, we can calculate an estimate with a 95% confidence interval for the proportion of voters who think competence is more significant than character:

CI equals p z*(sqrt(p*(1-p)/n)/p)).

where: p = the percentage of voters who say character is more essential than competence = 0.57; n = the sample size; 1000; and z = the z-score for a 95% confidence level; 1.96.

By entering the numbers, we obtain:

CI = 0.57 1.96*(sqrt(0.57*(1-0.57)/1000)), which equals 0.57 0.032. (0.538, 0.602)

the 95% confidence interval estimate for the proportion of respondents overall who think competence is more significant than character is (0.538, 0.602).

(B) Based on the range discovered in part, it is reasonable to infer that the majority of voters value competence over character (a). This is due to the interval's lower bound's value of 0.538, which is higher than 0.5. Therefore, we can state with 95% certainty that the actual proportion of voters who think competence is more crucial than character is at least 53.8%, which is a majority.

(C) In this instance, 95% confidence indicates that if the sampling procedure were repeated numerous times and a 95% confidence interval estimate was calculated for each sample, then roughly 95% of those intervals would contain the actual proportion of voters who believe competence is more significant than character. That is to say, we have a 95% confidence interval (0.538, 0.602) that contains the actual proportion of voters who think competence is more significant than character.

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The probability of the trials being successful is 0.625 or 62.5%. So, the expected value of Apnex stock after the announcement is $53.25 per share.

The odds of the trials being successful or failed, as well as the associated stock prices, must be taken into account in order to determine the predicted value of Apnex shares after the announcement.

we can state:

P(success) + P(failure) = 1

Let the market has already taken the probability into account and that the $56 stock price at the moment reflects the stock's anticipated value following the announcement. To put it another way, we can construct an equation based on the anticipated value formula:

Estimated Value = $68 for success and $18 for failure

Also, we are aware that the present stock price and the predicted value are equal:

Estimated Value = $56

When the second equation is substituted for the first equation, we obtain:

P(success) x $68 plus P(failure) x $18 equals $56.

For P(success), we obtain:

P(success) is equal to ($56 - $18) / ($68 - $18), or 0.625.

Thus, 0.625 or 62.5% of the trials will be successful.

We may determine the anticipated value of the shares following the announcement using this probability:

Estimated Value: 0.625 times $68 plus 0.375 times $18 equals $53.25

therefore, $53.25 per share is the anticipated value of Apnex shares following the announcement.

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The probability that client C, the 25-year-old you’re considering for a 30-year policy, lives to be 55 years old is 1.

The potential is implied by the word "probability". This area of mathematics studies how random events occur. The range is the set of values between 0 and 1. Probability has been incorporated into the mathematics to forecast the likelihood of various events. In essence, probability refers to the degree to which something is likely to occur. You can appreciate the possible results of a random experiment using this fundamental probability theory, which is also applied to a probability distribution. Before assessing how likely an event is to occur, we need to know how many possible outcomes there are.

Gerald age = 25 years

Policy considered = 30 years

Age at the end of the policy = 55 years

The probability that Geraldo lives to be 55 years will be:

= P(A + B)

= (25÷55) + (30÷55)

= 55÷55

= 1

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Using probability, we can find that the probability of getting a triangle shape block when selected at random is 1/5.

The chance of an event can be calculated using the probability formula by only dividing the favourable number of possibilities by the total number of potential outcomes.

The likelihood of an event occurring can be anything between 0 and 1, as the favourable number of outcomes can never exceed the total number of outcomes. Therefore, the percentage of successful results cannot be zero.

In the question,

Malaya has 5 different shapes of blocks.

Malaya has 10 blocks of each shape.

So, the total no. of blocks = 5 × 10 = 50.

Now, Malaya has 10 blocks of triangular shape.

probability of getting a triangular shape is:

P = 10/50

= 1/5

Therefore, the probability of getting a triangle shape block when selected at random is 1/5.

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The complete question is:

Malaya has 5different shapes of blocks: rectangle, rhombus, square, trapezoid, and triangle. She has 10 of each shape. She selects a block at random. What is the probability of getting a triangle shape block when selected at random?

According to the given conditions , the equation of the circle is [tex](x + 2)^2 + (y - 5)^2 = 16.[/tex]

What is circle ?

A circle is a two-dimensional geometric shape that consists of all points in a plane that are a fixed distance, called the radius, from a given point called the center. A circle can also be defined as the set of all points that are equidistant from a central point.

The equation of a circle with center (h, k) and radius r is:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

In this case, the center of the circle is (-2, 5) and the radius is 4, so the equation of the circle is:

[tex](x - (-2))^2 + (y - 5)^2 = 4^2[/tex]

Simplifying this equation gives:

[tex](x + 2)^2 + (y - 5)^2 = 16[/tex]

Therefore, according to the given conditions , the equation of the circle is [tex](x + 2)^2 + (y - 5)^2 = 16.[/tex]

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Answer:

i only know the answer (I guessed on but I think it's 70.65

Step-by-step explanation:

let me know if I'm right 0w0

Answer:

15 pounds

Step-by-step explanation:

for every 3 parts of dry fruit , four parts of nuts are added.
we know the total composition of the mixture is 35 pounds.


The total Composition of the mixture will be 7 parts

3/7 is dry fruit
4/7 is assorted nut


we can multiply the dry fruit composition to total
= 3/7 * 35 = 3*5 = 15

Pam needs 15 pounds of dry fruit to make the mixture.

After 5 days, the retailer starts making the money. The solution has been obtained by using the concept of break - even.

What is break - even?

The balance point known as "break-even" results in neither a profit nor a loss. Every value below the break-even mark represents a loss, whereas any value above it represents a gain.

We are given revenue function as R(x) = [tex]2x^3 + 11x^2 - 23x - 14[/tex].

The cost function is given as C(x) = [tex]13x^2 + 11x + 16[/tex].

The retailer will start earning only when the cost will be covered. This means that he will earn after when the R(x) = C(x).

So,

⇒ R(x) = C(x)

⇒ [tex]2x^3 + 11x^2 - 23x - 14[/tex] = [tex]13x^2 + 11x + 16[/tex]

⇒ [tex]2x^3[/tex] = [tex]2x^2 + 34x + 30[/tex]

⇒ [tex]x^3[/tex] = [tex]x^2 + 17x + 15[/tex]

⇒ [tex]x^3[/tex] - [tex]x^2 - 17x - 15[/tex] = 0

⇒ (x - 5) (x + 1) (x + 3) = 0

⇒ x = 5, -1, -3

Since, the days cannot be negative so, x = 5.

Hence, after 5 days, the retailer starts making the money.

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Question:

A popular video game retailer develops apps. The total revenue, in dollars per day, after x days can be modeled by the function R(x) = [tex]2x^3 + 11x^2 - 23x - 14[/tex]. The total cost, in dollars per day, after x days, can be modeled by the function C(x) = [tex]13x^2 + 11x + 16[/tex]. After how many days does the retailer start making money?

a. 1

b. 2

c. 5

d. 7

High Voltage, Inc. should use the following notation to construct its null and alternative hypotheses:                           Null Hypothesis: H0: μ1 - μ2 = 0; Alternative Hypothesis: H1: μ1 - μ2 ≠ 0; where μ1 represents the mean life span of High Voltage's product and μ2 represents the mean life span of the competitor's product.

The notation High Voltage should use to construct its null and alternative hypotheses is:

(i) Null Hypothesis: H0: μ1−μ2=0

where μ1 represents the mean life span of High Voltage's product and μ2 represents the mean life span of the competitor's product.

(ii) Alternative Hypothesis: Ha: μ1−μ2≠0

Where,μ1 and μ2 are the mean lifespan of the light bulbs of High Voltage and its competitor, respectively.

In this problem, paired samples t-test should be used to test the hypotheses.

Paired sample t-test: It is a statistical procedure used to compare two population means with two samples of dependent observations, where the dependent variable is the same or the same subject measured under different conditions. It is used when the observations are paired, i.e., each pair of observations consists of two measurements made on a single subject or item.

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zero

Observations are taken on sales of a certain mountain bike in 25 sporting goods stores. The regression model was Y= total sales (thousands of dollars), X 1 ​ = display floor space (square meters), X 2 ​ = competitors' advertising expenditures (thousands of dollars), X 3 ​ = advertised price (dollars per unit).Part a) the table is not given with the question. Please provide the required data and we will try our best to answer your question.The null and alternative hypotheses in a hypothesis test are:H0: βj = 0 Ha: βj ≠ 0j = 1, 2, 3. Since we have 3 predictors in the model so there will be three hypothesis test as well:Null and alternative hypotheses for hypothesis tests for β1, β2, and β3 are as follows:H0: βj = 0 Ha: βj ≠ 0j = 1, 2, 3.Therefore, if the absolute value of the computed t-value is greater than the absolute value of the table t-value for a specified α and n – k – 1 degrees of freedom, then the null hypothesis for that predictor is rejected. Hence, we can say that the predictor variable is significant at the α level.The table for t-values and p-values will be created based on the degree of freedom (d.f), the significance level (α), and the t-distribution function. The t-value is calculated using the following formula:t= (βi- 0) / SE(βi).Part b) Only CompetingAds differs significantly from zero is the correct option.

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The measure of angle A is equal to 41.11 rounded to two decimal place, using trigonometric ratio for the cosine of the angle A. The correct option is B.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

cos A = 55/73 {adjacent/hypotenuse}

A= cos⁻¹(55/73) {cross multiplication}

A = 41.1121

Therefore, the measure of angle A is equal to 41.11 rounded to two decimal place, using trigonometric ratio for the cosine of the angle A

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Answer: The y-intercept of the line of fit can be found by looking at the point where the line crosses the y-axis. From the given information, we know that the line passes through the points (0, 40) and (2, 70). To find the equation of the line, we can use the slope-intercept form:

y = mx + b

where m is the slope and b is the y-intercept. We can find the slope of the line by using the two points:

m = (y2 - y1) / (x2 - x1)

m = (70 - 40) / (2 - 0)

m = 30

So the equation of the line is:

y = 30x + b

To find the y-intercept, we can plug in one of the points and solve for b. Let's use the point (0, 40):

40 = 30(0) + b

b = 40

Therefore, the y-intercept of the line of fit is 40. In the context of the data, this means that a student who did not study at all (0 hours) is predicted to earn a grade of 40 on the test. However, it's important to note that this prediction is based on the data collected from the sample of 8 students and the line of fit may not accurately predict the grades of all students who did not study.

Your welcome.

The surface area of a triangular pyramid is the sum of areas of all faces of a triangular pyramid. Here, the surface area of a triangular pyramid with side 12 cm, base height 10 cm is equals to the 228 cm². So, the option (b) is correct choice.

Generally, a triangular pyramid has a triangular base and is bounded by three lateral triangular faces with one vertex. The units of measured surface area are square units like cm², m², ft² or cubit². The Formula for the surface area of a pyramid is calculated by adding up the area of all triangular faces of a pyramid. Mathematically,

Surface area = 1⁄2(a × b) + 3⁄2(b × s).

Where b --> the side of a pyramid

a --> the height of a base triangle, and

s --> the slant height of a pyramid. We have a triangular pyramid as present in above figure. Here height of base, a = 8 cm

slant height , s = 10 cm

side of a pyramid, b = 12 cm

So, Area of base triangle is, A1 = 1⁄2(a × b)

= (1/2)(8×12) = 48 cm²

Area of one triangular face = 1/2( b×s)

= 1/2( 12 × 10) = 60 cm²

Area of all triangular faces of a pyramid, A2 = 3× 60 = 180 cm²

The surface area of a pyramid = A1 + A2

= 48 + 180 = 228 cm²

Hence, required area is 228 cm².

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Complete question:

Find the surface area of the equilateral triangular pyramid. See the above

A 180cm^2

B 228cm^2

C 268cm^2

D 456cm^2

The polar form of the quantity will be  100.83 L 76.47°.

Given X = 5 L 40'andY = 20 L -30°(X + Y)X* .The expression (X + Y)X* can be simplified as: X * X + Y * X* =X² + Y * X* .Now, we need to find the polar form of the quantity (X + Y)X*.That is, we need to representX² + Y * X* in polar form. By using rectangular to polar conversion, we can convert the above expression to polar form.

Using the formula:

r² = x² + y²... Equation 1

θ = tan⁻¹(y / x)... Eq 2 (Where,x = real part of the expression)

x = X² = 5² = 25... Eq 3 (y = imaginary part of the expression)

y = Y * X*... Eq 4

Therefore, Y

Y * X* = 20 L -30° * 5 L 40'20 L -30° * 5 L 40' = 100 L 10°... Eq5

y = 100 L 10°.

Substituting the values of x and y in equations 1 and 2, we get:r² = x² + y²r² = 25² + 100²r² = 10025 + 100²r = 100.83θ = tan⁻¹(y / x)θ = tan⁻¹(100 L 10° / 25)θ = tan⁻¹(4 L 10°)θ = 76.47°

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To find the dimensions of a parallelogram, you need to know the length of its base and the perpendicular distance from the base to the opposite side, which is also called the height or altitude of the parallelogram.

A quadrilateral (a four-sided polygon) with two pairs of parallel sides is referred to as a parallelogram. This means that the opposite sides of the parallelogram are parallel and have the same length, while the adjacent sides are unequal in length.

The properties of a parallelogram include:

The opposing sides seem to be congruent and parallel (equal in length)

Congruent opposite angles (equal in measure)

The angle adjacent to each other are supplementary (their sum is 180 degrees)

Diagonals bisect each other (the diagonals divide each other into two equal parts)

If you have the measurements of the sides and angles of the parallelogram, you can use trigonometry and geometry to find the length of the base and the height. For example, if you have the lengths of two adjacent sides and the angle between them, you can use the sine function to find the height. The base can be found by using the formula for the area of a parallelogram, which is base times height.

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Answer:

A = P(1 + r/n)^(nt)

Where:

A = the final amount

P = the initial balance

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

We know that P = $3500, A = $4390.40, r = unknown, n = 1 (compounded annually), and t = 2. Plugging in these values and solving for r:

$4390.40 = $3500(1 + r/1)^(1*2)

$4390.40/$3500 = (1 + r)^2

1.2544 = (1 + r)^2

√1.2544 = 1 + r

1.12 = 1 + r

r = 0.12 or 12%

Therefore, the annual interest rate is 12%.