A triangular window is above the door to a café. The base of the window is 12 feet, and the height is 10 feet.



What is the area of the window?

Enter your answer in the box.

a) The recurrence relation for the amount in the account  paying 4%, compounded annually at the end of n years with is \(S(n)=1.04^n*S(0)\).

b) The amount of money at end of 4 years is $5849.29

a)

Given,

Amount of money deposited into account with interest 4% compounded annually.

If s(n) is the total amount in  account after n years and S(0) is the initial amount deposited then the recurrence relation can be written as,

\(S(n) = S(n-1) +0.04*S(n-1)\\\\\)      

where 4% = 0.04

\(S(n) = 1.04*S(n-1)-------eq(1)\)

replacing n by n-1 in eq (1)

\(S(n-1) = 1.04*S(n-2))\\\\S(n)=1.04*1.04*S(n-2)\\\\S(n)=1.04^2*S(n-2)\)

replacing n by n-2 in eq (1),

\(S(n-2) = 1.04*S(n-3)\\\\S(n)=1.04^3*S(n-3)\)

then general equation for n years can be written as

\(S(n)=1.04^n*S(n-n)\\\\S(n)=1.04^n*S(0)\)

b)

using above formula,

Let S(0) represent the $5,000 initial deposit then S(4) represent the amount in the bank after 4 years.

\(S(4) = 1.04^4*S(0)\\\\S(4)=1.1698585*5000=5849.292\)

Thus, the amount of money at the end of 4 years is $5849.29

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In triangle ABC, Length of DE = (a*x)/(b+c). We can use similarity of triangles  to to get the proportion between corresponding sides.

Similarity of triangles can help us to relate the lengths AB, DE, BE, and EC.

Now, since, DE =  (a*x)/(b + c) in terms of a, b and c(given).

Now, we can relate the corresponding sides of triangle ABC and ADE.

The denominator (b + c) is equal to the sum of the lengths BE and EC.

Therefore, to express x in terms of a, b, c when in triangle ABC, DE || AB, and AB = a, DE = x, BE = b and EC = c.

DE = (a*x)/(b + c).

This question uses similarity of triangles which is a geometric concept. It helps us to correspond two triangles with different shapes and sizes, and when two triangles are similar their ratios of lengths is proportional to each other.

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Convenience purchase: Coca-Cola. Shopping purchase: Apple iPhone. Specialty purchase: Rolex. These brand name products correspond to their respective purchase types based on convenience, shopping involvement, and specialty appeal in the consumer marketplace.

Convenience purchases refer to low-involvement purchases made by consumers for everyday items that are readily available and require minimal effort to obtain. These purchases are typically driven by convenience and habit rather than extensive consideration or brand loyalty.

Shopping purchases involve higher involvement and more deliberate decision-making. Consumers invest time and effort in comparing options, seeking the best value or quality, and may consider multiple brands before making a purchase. These purchases often involve durable goods or products that require more consideration.

Specialty purchases are distinct and unique purchases that cater to specific interests, preferences, or hobbies. These purchases are driven by passion, expertise, and a desire for premium or specialized products. Consumers are often willing to invest more in these purchases due to their unique features, quality, or exclusivity.

Three specific brand name products in the consumer marketplace that correspond to these types of purchases are

Convenience Purchase: Coca-Cola (Soft Drink)

Coca-Cola is a widely recognized brand in the beverage industry. It is readily available in various sizes and formats, making it a convenient choice for consumers seeking a refreshing drink on the go.

With its widespread availability and strong brand presence, consumers often make convenience purchases of Coca-Cola without much thought or consideration.

Shopping Purchase: Apple iPhone (Smartphone)

The Apple iPhone is a popular choice for consumers when it comes to shopping purchases. People invest time researching and comparing features, pricing, and user reviews before making a decision.

The shopping process involves considering various smartphone brands and models to ensure they select a product that meets their specific needs and preferences.

Specialty Purchase: Rolex (Luxury Watches)

Rolex is a well-known brand in the luxury watch industry and represents specialty purchases. These watches are associated with high-quality craftsmanship, precision, and exclusivity.

Consumers who are passionate about luxury watches and seek a premium product often consider Rolex due to its reputation, heritage, and unique features. The decision to purchase a Rolex involves a significant investment and is driven by the desire for a prestigious timepiece.

These examples illustrate how different types of purchases align with specific brand name products in the consumer marketplace, ranging from convenience-driven choices to more involved shopping decisions and specialty purchases driven by passion and exclusivity.

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The smallest perimeter is P = 2L + 2W = 2(2) + 2(2) = 8 in, and the dimensions of the rectangle are 2 in by 4 in.

To find the smallest perimeter for a rectangle with an area of 4 in² using derivatives, we can set up an optimization problem. Let's denote the length of the rectangle as L and the width as W.

The formula for the area of a rectangle is given by A = L × W. Since we know the area is 4 in², we can write the equation as 4 = L × W.

To find the smallest perimeter, we need to minimize the perimeter function P = 2L + 2W while satisfying the area constraint.

We can rewrite the area equation as W = 4/L and substitute it into the perimeter equation to get P = 2L + 2(4/L).

Now, we find the derivative of the perimeter function with respect to L: \($dP/dL = 2 - \frac{8}{L^2}$\).

To find the minimum perimeter, we set the derivative equal to zero and solve for L:

\(2 - \frac{8}{L^2} = 0\\\\ 2 = \frac{8}{L^2}\\\\ L^2 = \frac{8}{2}\\\\ L^2 = 4\\\\ $L = \pm 2$\)

Since we're dealing with lengths, we take L = 2 (we discard the negative solution). Substituting this value back into the area equation, we find W = 4/L = 4/2 = 2

Therefore, the smallest perimeter is P = 2L + 2W = 2(2) + 2(2) = 8 in, and the dimensions of the rectangle are 2 in by 4 in.

Now, consider finding the largest perimeter. Since we're not given any constraints on the dimensions, the largest perimeter is unbounded and not defined for a fixed area of 4 in². As one side of the rectangle approaches infinity, the perimeter also approaches infinity. Therefore, there is no upper limit to the perimeter.

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The answers to the questions involving trigonometry are: 90, BC/AB ÷ BC/AB = 1, g = 6.5, <I = 62 degrees, h= 13.8, 12.0, x = 6.8, x = 66.4, 160.6, The pole = 6.7

Trigonometric ratios are special measurements of a right triangle, defined as the ratios of the sides of a right-angled triangle.  There are three common trigonometric ratios: sine, cosine, and tangent

For page 3 question 3,

a) <A + <B = 90 since <C = right angle

b) SinA = BC/AB and CosB = BC/AB

The ratio of the two angles BC/AB ÷ BC/AB = 1

I notice that the ratio of sinA and cosB gives 1

b) The ratio of CosA and SinB will give

BC/AB ÷ BC/AB

= BC/AB * AB/BC = 1

For page 5 number 3

Tan28 = g/i

g/12.2 = tan28

cross multiplying to have

g = 12.2*tan28

g = 12.2 * 0.5317

g = 6.5

b) the angle I is given as 90-28 degrees

<I = 62 degrees

To find the side h we use the Pythagoras theorem

h² = (12.2)² + (6.5)²

h² = 148.84 +42.25

h²= 191.09

h=√191.09

h= 13.8

For page 6

1) Sin42 = x/18

x=18*sin42

x = 18*0.6691

x = 12.0

2) cos28 = 6/x

xcos28 = 6

x = 6/cos28

x [= 6/0.8829

x = 6.8

3)  Tan63 = x/34

x = 34*tan63

x= 34*1.9526

x = 66.4

4) Sin50 123/x

xsin50 = 123

x = 123/sin50

x = 123/0.7660

x =160.6

5)  Sin57 = P/8

Pole = 8sin57

the pole = 8*0.8387

The pole = 6.7

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Answer:

If the circular track has a circumference of 0.5 mile, then its circumference in feet is:

0.5 mile x 5,280 feet/mile = 2,640 feet

The formula for the circumference of a circle is:

C = 2πr

where C is the circumference and r is the radius of the circle. Substituting the values we have:

2,640 = 2 x 3.14 x r

Solving for r, we get:

r = 2,640 / (2 x 3.14) = 420.38 feet

Therefore, the radius of the circular track, in feet, is approximately 420.38 feet. Rounded to the nearest hundredth, the answer is 420.38 feet, which corresponds to the third option.

\( \large \mathfrak{Solution : }\)

let's solve for f(-9) :

Step-by-step explanation:

that's all

thank you

The given exponential function equation is A = P(1+r)t, where P represents the principal amount, A represents the final amount, r represents the annual interest rate, and t represents the time in years.a.

The independent variable is t (time in years) while the dependent variable is A (final amount).b. The growth factor can be obtained by dividing A by P. Therefore, Growth factor = A/PLet us assume P=100, r=20%, and t=1. Then we can find A as follows:A = P(1+r)tA = 100(1+0.2)1A = 100(1.2)A = 120Therefore, the growth factor is:A/P = 120/100 = 1.2If we assume P=150, r=5%, and t=2, thenA = P(1+r)t = 150(1+0.05)2= 150(1.1025)= 165.375The growth factor is:A/P = 165.375/150 = 1.1025

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Answer:

125

Step-by-step explanation:

El Angulo suplementario es cuando los ángulos sumados valen 180.

Ejemplo: Angulo suplementario de 15.

15+x=180

x=180-15

x=165

Entonces:

180=55+X

180-55=X

125=X

Respuesta: 125

Answer:

Yes

Step-by-step explanation:

10x + 2y > 3

Substitute the point into the inequality

10(4)+2(3) > 3

40+6>3

46>3

This is a true statement so the point is a solution

Step-by-step explanation:

sorry but I dont know

Answer: 654 grams

Step-by-step explanation:

that's the answer it gave it when I got it wrong.

Answer:

Step-by-step explanation:

The verbiage "five and nine tenths" can refer to the mixed number 5 9/10, or to the decimal in standard form, 5.9. Simply converting the phrase to a decimal gets you the standard form.

The expanded form can be written a number of ways, depending on how you like to show the place value multipliers. The simplest expanded form is simply the sum of the digits:

  5 + 0.9

You can show the multipliers in standard form:

  5×1 + 9×0.1

Or, you can show the multipliers in exponential form:

  5×10⁰ +9×10⁻¹

Answer:

the answer is (x )

math  way  helps

Step-by-step explanation:

The requried function of function f(g(x)) is given as x² + 6x +5.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

here,
Given functions,
f(x)=x²−4 and g(x)=x+3

In order to form a function of function we have to function g(x) in function f(x)

Now,

f(g(x)) =  f(x)=(g(x))²−4

f(g(x)) =  f(x)=(x+3)²−4
f(g(x)) = x² + 6x + 9 -4
f(g(x)) = x² + 6x +5

Thus, the requried function of function f(g(x)) is given as x² + 6x +5.

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Answer:

Its 68 because left side is 20 right side is 20 and top and bottom are both 8 and the back and front are 10

Counting from point M (0 unit) on this number line, we can logically deduce that point H is located at -7.

A numerical data is also referred to as a quantitative data and it can be defined as a data set that is primarily expressed in numbers only. This ultimately implies that, a numerical data refers to a data set consisting of numbers rather than words.

In Mathematics, there are six (6) common types of numbers and these include the following:

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length. Also, the negative numerical values are positioned at the left from zero while the positive numerical values are positioned at the right from zero.

Note: Each of the tick represents 1 unit.

Therefore, counting from point M (0 unit) on this number line, we can logically deduce that point H is located at -7.

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The measurement of angle DBC is equal to 33°, here we have to know the meaning of angle.

Angle is the measurement distance between two straight line or ray when they meet and it can also say that their one part is opening and other part is joint.

We have given that, ∠ABD = 4x, ∠DBC = 3x and measure of angle ABC is equal to 77°.

So ∠ABD + ∠DBC = ∠ ABC

⇒  4x + 3x = 77°

⇒ 7x = 77°

⇒ x = 11°

So, ∠ ABD = 4x = 4 * 11 = 44°

and, ∠DBC = 3x = 3 * 11 = 33°

Therefore, angle DBC is equal to 33°.

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Complete Question:

What is the measure of angle DBC if the measure of angle ABD is represented by 4x, the measure of angle DBC is represented by 3x and the measure of angle ABC is 77° ?

Answer:

Question 1: b) Find the total distance from A to B

Distance formula:

d=Square root of (x2-x1)^2+(y2-y1)^2+(z2-z1)^2

d=Square root of (6-4)^2+(12-8)^2+(10-2)^2

d= 9.165 = 9.17 units

Answer:

1 a

Use the midpoint formula:

m=x1+x2/2, y1+y2/2, z1+z2/2

m= 4+6/2 ,8+12/2, 2+10/2

m= (5 ,10, 6)

Step-by-step explanation:

Answer:

There are 4 terms

Step-by-step explanation:

“Terms are single numbers, variables, or the product of a number and variables. Examples of terms: 9 a 9a 9a. y y y.”

We can model this with a binomial random variable, with sample size n=4 and probability of success p=1/6.

As we have to calculate the probability of getting at least one 2, it is easy to substract from a probability equal to 1 the probability of getting no 2. This can be written as:

The probability of getting at least one 2 in dice rolled 4 times is P=671/1296.

Mean of the Sampling Distribution: Mean of the Sampling Distribution of the sample proportion is p = 0.76.Standard Deviation of the Sampling Distribution: For calculating the standard deviation of the Sampling Distribution of the sample proportion, we use the following formula:

σp = sqrt[p(1 - p) / n]σp = sqrt[0.76(1 - 0.76) / 58]σp = 0.0639

As per the given question, we can determine the mean and standard deviation of the sampling distribution or sample proportion of schools stating students starting school in 2020 needed more communication support than in previous years as below:

Mean of the Sampling Distribution: Mean of the Sampling Distribution of the sample proportion is p = 0.76.Standard Deviation of the Sampling Distribution: For calculating the standard deviation of the Sampling Distribution of the sample proportion, we use the following formula:σp = sqrt[p(1 - p) / n]σp = sqrt[0.76(1 - 0.76) / 58]σp = 0.0639The probability that the sample proportion of schools stating students starting school in 2020 needed more communication support than in previous years is greater than 70% can be determined as below:First, we calculate the z-score of 0.70 as:z = (0.70 - 0.76) / 0.0639z = -0.94The probability that the sample proportion is greater than 0.70 is equal to the probability of a z-score being greater than -0.94. By looking up in the normal distribution table, the probability of a z-score being greater than -0.94 is 0.8242.

Therefore, the probability that the sample proportion of schools stating students starting school in 2020 needed more communication support than in previous years is greater than 70% is 0.8242.The probability that the sample proportion of schools stating students starting school in 2020 needed more communication support than in previous years is between 50% and 80% can be determined as below:First, we calculate the z-scores of 0.50 and 0.80 as:z1 = (0.50 - 0.76) / 0.0639z1 = -4.07z2 = (0.80 - 0.76) / 0.0639z2 = 0.63The probability that the sample proportion is between 0.50 and 0.80 is equal to the probability of z-score being between -4.07 and 0.63. By using the normal distribution table, the probability of a z-score being between -4.07 and 0.63 is 0.9957. Therefore, the probability that the sample proportion of schools stating students starting school in 2020 needed more communication support than in previous years is between 50% and 80% is 0.9957.

In the given question, we have calculated the mean and standard deviation of the sampling distribution or sample proportion of schools stating students starting school in 2020 needed more communication support than in previous years. Further, we have also calculated the probability that the sample proportion of schools stating students starting school in 2020 needed more communication support than in previous years is greater than 70% and the probability that the sample proportion of schools stating students starting school in 2020 needed more communication support than in previous years is between 50% and 80%.

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Answer:

Step-by-step explanation:

compare with y=mx+b

m=-1

b=4

(b)

area of triangle=1/2×4×4=8 square units.

Answer:

below

Step-by-step explanation:

9c + 6a = total cost

The circle with center (0,6) containing the point (74,2) has an equation of x² + (y - 6)² = 74.1²

The equation of a circle is:

(x - h)² + (y - k)² = r²

Where (h, k) is the center and r is the radius.

The circle with center (0,6) containing the point (74,2). Hence:

\(Radius=\sqrt{(2-6)^2+(74 -0)^2}=74.1\ unit\)

The equation is:

x² + (y - 6)² = 74.1²

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Based on the exponential decay function, the resale of the car purchased for $16,500 and whose value decreases by 30% annually will be $5,659.50 after 3 years.

The exponential function is the mathematical function written as y = abˣ.

The y and x are variables.  The "a" and "b" are constants.

There are two types of exponential functions, namely exponential growth and exponential decay.

In this situation, we are dealing with an exponential decay function because there is a constant rate of decrease per year.

The purchase value of the car = $16,500

Annual rate of decrease in value = 30%

Period of decrease = 3 years

The value of the car after 3 years = y

y = 16,500 x (1 - 30%)³

y = 16,500 x 0.7³

y = 16,500 x 0.343

y = $5,659.50

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Answer:

This is your answer ☺️

Answer:

7/50

Step-by-step explanation:

The probability of drawing an odd number or a number more than 7 is given as follows:

p = 1/2.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is then calculated as the division of the number of desired outcomes by the number of total outcomes.

The total number of outcomes is given as follows:

2 x 7 = 14.

Out of those, we have 7 desired outcomes, hence the probability is given as follows:

p = 7/14

p = 1/2.

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what 5x10 = 50

60x 10 =600

30x1 =30

1x1=1

2x2=4

Answer:

Step-by-step explanation: shyweydehdeecebccecjeejddijde shut the f

We have proved that 1*1! + 2*2! + ... + n*n! = (n + 1)! -1 is true for all positive integers n.

Given expression is: 1*1! + 2*2! + ... + n*n! = (n + 1)! -1

We need to prove this equation for n positive integers.

Let's prove this by induction, Base Case:

For n=1,

1*1! = (1+1)! - 1

=> 1 = 2 - 1

=> 1 = 1

The base case is true.

Inductive Step:

Let's assume that the given expression holds for some k, that is:

1*1! + 2*2! + ... + k*k! = (k + 1)! - 1

Now we will prove that the same equation holds for k+1, that is:

1*1! + 2*2! + ... + (k+1)*(k+1)! = (k + 2)! - 1

By using the inductive hypothesis, we can replace the sum up to k with (k+1)! - 1, that is:

(k+1)! - 1 + (k+1)*(k+1)! = (k+1)! - 1 + (k+1)!

We can take (k+1)! common from the above equation. That is:

(k+1)![(k+1) - 1 + 1] = (k+1)! * (k+2) => (k+2)! - (k+1)!

= (k+1)! * (k+2) - (k+1)!

= (k+1)!(k+2-1)

= (k+1)!*k+1

That is: 1*1! + 2*2! + ... + (k+1)*(k+1)! = (k + 2)! - 1

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