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The exponential function giving the balance of the account after t months is:

[tex]y = 100(1.02)^t[/tex]

The yearly growth factor is given as follows:

26.82%.

An exponential function has the definition presented as follows:

[tex]y = ab^x[/tex]

In which the parameters are given as follows:

The parameter values for this problem are given as follows:

Hence the function is:

[tex]y = 100(1.02)^t[/tex]

The yearly growth factor can be obtained as follows:

[tex](1.02)^{12} = 1.2682[/tex]

Increase of 26.82% each year, which is composed by 12 months.

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Both equations give the correct terms, so we can conclude that the pattern rule is:  [tex]an^2 - 131n + 80[/tex] , where [tex]a=63[/tex]  .

To find the pattern rule for the given sequence 12, 59, 294, 1469, 7344, we need to observe the differences between consecutive terms. Let's find the differences between each pair of terms:

[tex]59 - 12 = 47[/tex]

[tex]294 - 59 = 235[/tex]

[tex]1469 - 294 = 1175[/tex]

[tex]7344 - 1469 = 5875[/tex]

The differences are not constant, so we need to find the differences between these differences:

[tex]235 - 47 = 188[/tex]

[tex]1175 - 235 = 940[/tex]

[tex]5875 - 1175 = 4700[/tex]

Now, the second differences are constant (equal to 940), which suggests that the pattern rule is a quadratic equation. Let's assume the pattern rule is of the form:

[tex]an^2 + bn + c[/tex]

where n is the term number (starting with n=1 for the first term).

To find the coefficients a, b, and c, we can use the first three terms of the sequence. Let's substitute n=1,2,3 into the equation and equate it to the corresponding terms:

[tex]a + b + c = 12 (for n=1)[/tex]

[tex]4a + 2b + c = 59 (for n=2)[/tex]

[tex]9a + 3b + c = 294 (for n=3)[/tex]

We can solve these equations simultaneously to get the values of a, b, and c:

[tex]a = 63[/tex]

[tex]b = -131[/tex]

[tex]c = 80[/tex]

Therefore, the pattern rule for the sequence is:

[tex]an^2 - 131n + 80[/tex]

where a=63.

To check if this pattern rule works for the other terms of the sequence, we can substitute n=4 and n=5:

[tex]a(4^2) - 131(4) + 80 = 1469[/tex]

[tex]a(5^2) - 131(5) + 80 = 7344[/tex]

Therefore, Both equations give the correct terms, so we can conclude that the pattern rule is:

[tex]an^2 - 131n + 80, where a=63.[/tex]

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Check the picture below.

The equation of the line passing through the points (-7, -3) and (1, 2) is [tex]y = \frac{5}{8}x + \frac{11}{8}[/tex].

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

First, we determine the slope of the line.

Given the two points are (-7, -3) and (1, 2)

We can find the slope of the line by using the slope formula:

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values, we get:

m = (2 - (-3)) / (1 - (-7))

m = 5/8

Using the point-slope form, plug in one of the given points and slope m = 5/8 to find the equation of the line.

Let's use the point (-7, -3:

y - y₁ = m(x - x₁)

[tex]y - (-3) = \frac{5}{8}( x - (-7) ) \\\\y + 3 = \frac{5}{8}(x + 7 )\\\\y + 3 = \frac{5}{8}x + \frac{35}{8} \\ \\y = \frac{5}{8}x + \frac{35}{8} - 3\\\\y = \frac{5}{8}x + \frac{11}{8}[/tex]

Therefore, the equation of the line is [tex]y = \frac{5}{8}x + \frac{11}{8}[/tex].

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Answer:

x = 65

Step-by-step explanation:

let the number be 'x'.

If 86 is added to a number, the result is 44 less than three times the number. Therefore the equation will be,

=> 86 + x = 3x - 44

Rearranging,

=> x - 3x = -44 - 86

=> -2x = -130

=> x = 130/2

=> x = 65

Answer:

[tex]f(t) = 8e^{0.223144t}[/tex]

Answer:

Step-by-step explanation:

it should be shaded at the 76

Step-by-step explanation:

m=y1-y2/x1-x2

m=2-8/5-8

m=-6/-3

m=2

y=m(x-x1)+y1

y=m(x-8)+8

y=2x-16+8

y=2x-22

Answer: Y=mx+c

Step-by-step explanation:

The Slope-Intercept Form can be written in the form: y = mx + c Where “m” is the slope of the line “c” is the y-intercept of the equation of the line

Answer:

I put the answer on the attachment please look

In ΔFGH,  the length of h is 714.2 cm

Let us assume that in ΔFGH, f represents the opposite side to angle F, g represents the opposite side to angle G,  and h represents the opposite side to angle H.

Consider the following figure.

Using sine rule for triangle FGH,

sin F/f = sin G/g = sin H/h

Consider equation sin G/g = sin H/h

sin(98°) / 910 = sin(51°) / h

We solve this equation for h.

h = (sin(51°) × 910)/ sin(98°)

h =  (0.777 × 910)/ 0.99

h = 714.21

h = 714.2 cm

This is the required length of h.

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the first mechanic charged $55 per hour and the second mechanic charged $100 per hour. we solve this by forming equation by by given data.

what is equation ?

An equation is a mathematical statement that shows that two expressions are equal. It typically consists of two sides separated by an equal sign (=). The expressions on each side of the equal sign can contain variables,

In the given question,

Let's assume that the first mechanic charged x dollars per hour and the second mechanic charged y dollars per hour.

From the problem, we know that:

The first mechanic worked for 20 hours, so he charged 20x dollars.

The second mechanic worked for 15 hours, so he charged 15y dollars.

Together, they charged a total of $2600, so we have:

20x + 15y = 2600

The sum of the two rates was $155 per hour, so we have:

x + y = 155

We can use these two equations to solve for x and y. First, we can rewrite the second equation as:

y = 155 - x

Then, we can substitute this expression for y into the first equation:

20x + 15(155 - x) = 2600

Simplifying and solving for x, we get:

20x + 2325 - 15x = 2600

5x = 275

x = 55

Now that we know x, we can use the second equation to find y:

y = 155 - x = 155 - 55 = 100

Therefore, the first mechanic charged $55 per hour and the second mechanic charged $100 per hour.

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The claim is: Testing if the time spent completing the obstacle course is improved by the energy drink

The null and the alternate hypotheses are added below

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

The table

Also, we have the following statistical question

Is there sufficient evidence at α = 0.05 to conclude that the students did better the second time?

This means that the null hypothesis are

H1: There is no significant difference in the time spent to complete the obstacle course before and after drinking the new energy drink.

The alternate hypothesis is the opposite of the null hypothesis

So, we have

H2: There is no significant difference in the time spent to complete the obstacle course before and after drinking the new energy drink.

Lastly, the claim is that

Testing if the time spent completing the obstacle course is improved by the energy drink

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In this case, the cube root is = 0

We can use the rule Sarrus to evaluate the determinant

1 w w²

w w² 1

w² 1 w

Starting with the first column, we can wrte out the terms for the diagonal products and

then sum the terms for the products of the diagonal elements that wrap around

(1 x w² x  w) +(w x 1 x w²) + (w² x w x w)    - (w ² x w x 1) - (w x w² x w) - (1 x w x w ²)

Simplifying each term:

w³ +   w³ + w³ -   w³ -w³   - w³

We can see that all the terms cancel   out, leaving us with a determinant of 0. So it is clear that

|1 w w²|

|w w² 1 |

|w² 1 w | = 0

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Evaluate the determinant 1 w w2 , w w2 1, w2 1 w. where w is a cube root of unity.

The result of the division of the two complex numbers is equal to z₁ / z₂ = (8 / 9) · [cos (π / 10 - π / 12) + i sin (π / 10 - π / 12)].

In this problem we find two complex numbers in rectangular form, whose division must be found. This can done by easily by means of complex numbers in polar form and definition of division:

Complex number (rectangular form)

z = r · (cos θ + i sin θ)

Complex number (polar form)

[tex]z = r\cdot e^{i\cdot \theta}[/tex]

Where:

Division between two complex numbers in polar form:

[tex]\frac {z_{1}}{z_{2}} = \left(\frac{r_{1}}{r_{2}}\right)\cdot e^{i\cdot (\theta_{1}-\theta_{2})}[/tex]

This number is equivalent to the following expression in rectangular form:

z₁ / z₂ = (r₁ / r₂) · [cos (θ₁ - θ₂) + i sin (θ₁ - θ₂)]

If we know that r₁ = 8, r₂ = 9, θ₁ = π / 10 and θ₂ = π / 12, then the division of the two complex numbers is:

z₁ / z₂ = (8 / 9) · [cos (π / 10 - π / 12) + i sin (π / 10 - π / 12)]

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The solution for x is -48, the answer is D) -48.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. It represents a value that can change based on the values assigned to the variables.

Starting with:

x:4 = 12

Multiplying both sides by -1 gives:

(-x÷4) = -12

Simplifying the left side:

x÷4 = -12

Multiplying both sides by 4 gives:

x = -48

Therefore, the solution for x is -48, the answer is D) -48.

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The value of the variable w is 56

Algebraic expressions are described as expressions that are composed of terms, variables, factors, coefficients and constants.

Also, algebraic expressions are made up of mathematical or arithmetic operations, such as;

From the information given, we have the algebraic equation as;

w - 54 = 2

To determine the value of the variable, we take the steps;

collect the like terms

w = 2 + 54

Now, add the values

w = 56

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We can rearrange the formula to solve for h:

v = √√2gh

Squaring both sides: v^2 = 2gh

Dividing both sides by 2g: h = v^2 / 2g

Substituting v = 96 ft/s and g = 32 ft/s^2, we get:

h = (96 ft/s)^2 / (2 × 32 ft/s^2)

h = 288 ft

Therefore, the object has fallen 288 feet.

The horizontal asymptotes of the function is y = 0 and the y-intercepts is (0, 1).

An exponential graph is a curve that represents an exponential function. An exponential graph is a curve that has a horizontal asymptote and it either has an increasing slope or a decreasing slope. i.e., it starts as a horizontal line and then it first increases/decreases slowly and then the growth/decay becomes rapid.

In this problem, the graph of the function f(x) = (1/4)ˣ is attached below the question and the characteristics of the graph are;

1. The domain of the function is {x|x ∈ R}

2. The range of the function is {y|y > 0}

3. The horizontal asymptotes is y = 0

4. The x-intercepts does not exists

5. The y-intercepts are (0, 1)

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Answer:

see below

Step-by-step explanation:

The Reason for #1 is literally GIVEN to you.

Statement #2: Since the Base Angles of an isosceles triangle are congruent, this statement should be ∠CAB≅∠CBA.

Reason #3: Notice that the statement repeats itself (AB=AB). This demonstrates the REFLEXIVE property.

Reason #4: (Clue) Note which items have been Given or Proven congruent and use it as the triangle congruence property. It helps to actually mark them. Your choices are SSS, SAS, ASA, and AAS.

Reason #5: (Clue) Since the triangles of which AM and BN are of part are now proven congruent, these Corresponding Parts are Congruent as well.

Answer:

429  i think

Step-by-step explanation:

a) The probability of selecting exactly 3 award-winners before selecting a SENIOR is  0.078875

b)The probability of selecting more than 2 award-winners before selecting a JUNIOR is 0.135437

c)The probability of selecting 2 or fewer award-winners before selecting a SOPHOMORE is 0.252744

Probability is a measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain to occur.

(a) The probability of selecting a SENIOR is 0.65, and the probability of not selecting a SENIOR is 0.35.

Since we are selecting award-winners until we select a SENIOR, the first two selections must not be SENIORS, and the third selection must be a SENIOR.

the probability of selecting exactly 3 award-winners before selecting a SENIOR is:

P(not SENIOR) x P(not SENIOR) x P(SENIOR) = 0.35 x 0.35 x 0.65 = 0.078875

(b)Therefore, the probability of selecting more than 2 award-winners before selecting a JUNIOR is:

P(not JUNIOR) x P(not JUNIOR) x P(JUNIOR) = 0.77 x 0.77 x 0.23 = 0.135437

To find the probability of selecting more than 2 award-winners, we can subtract this value from 1, since the only other possibility is selecting exactly 2 award-winners before selecting a JUNIOR:

P(more than 2) = 1 - P(exactly 2) = 1 - (P(not JUNIOR) x P(JUNIOR) x P(not JUNIOR)) = 1 - (0.77 x 0.23 x 0.77) = 0.567911

(c) The probability of selecting a SOPHOMORE is 0.12, and the probability of not selecting a SOPHOMORE is 0.88.

Since we are selecting award-winners until we select a SOPHOMORE, we can keep selecting SENIORS and JUNIORS until we select a SOPHOMORE.

Therefore, the probability of selecting 2 or fewer award-winners before selecting a SOPHOMORE is:

P(SOPHOMORE) + P(not SOPHOMORE) x P(JUNIOR) x P(SOPHOMORE) + P(not SOPHOMORE) x P(not JUNIOR) x P(JUNIOR) x P(SOPHOMORE) = 0.12 + (0.88 x 0.23 x 0.12) + (0.88 x 0.77 x 0.23 x 0.12) = 0.252744

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a) Based on the first derivative test, h(x) has a relative minimum at x = -2 and a relative maximum at x = 0.

b)  For x = -2: h''(-2) = 6(-2) + 6 = -6 < 0, so h(x) has a relative maximum at x = -2.

For x = 0: h''(0) = 6(0) + 6 = 6 > 0, so h(x) has a relative minimum at x = 0.

Calculus is a branch of mathematics that deals with the study of rates of change, accumulation, and the properties and behavior of functions.

(a) First derivative test:

The first derivative test involves finding the critical points of the function, where the first derivative is equal to zero or undefined, and then checking the sign of the first derivative in the intervals between the critical points to determine whether the function has relative extrema at those points.

Find the first derivative of h(x):

h'(x) = 3x² + 6x

Set h'(x) = 0 and solve for x to find the critical points:

3x² + 6x = 0

x(x + 2) = 0

x = 0 or x = -2

Test the intervals between the critical points using the sign of the first derivative:

For x < -2: Choose x = -3, h'(-3) = 27 + (-18) = 9 > 0, so h(x) is increasing.

For -2 < x < 0: Choose x = -1, h'(-1) = 3 - 6 = -3 < 0, so h(x) is decreasing.

For x > 0: Choose x = 1, h'(1) = 3 + 6 = 9 > 0, so h(x) is increasing.

Based on the first derivative test, h(x) has a relative minimum at x = -2 and a relative maximum at x = 0.

(b) Second derivative test:

The second derivative test involves finding the critical points of the function using the first derivative, and then checking the sign of the second derivative at those points to determine whether the function has relative extrema at those points.

Find the second derivative of h(x):

h''(x) = 6x + 6

Evaluate the second derivative at the critical points found in step 2 of the first derivative test:

For x = -2: h''(-2) = 6(-2) + 6 = -6 < 0, so h(x) has a relative maximum at x = -2.

For x = 0: h''(0) = 6(0) + 6 = 6 > 0, so h(x) has a relative minimum at x = 0.

Hence, the ease of a test may vary for different individuals and their familiarity with calculus concepts.

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Answer:

{3, 6, 9, 12, 15}

Each of these numbers is divisible by 3

Step-by-step explanation:

Answer:

O (x + 1)2 + (y + 2)² = 9

Step-by-step explanation:

This is because the distance between points A and B is 3 units, and the distance between points B and C is 4 units, making the triangle a 3-4-5 right triangle. Point B is located at (-1, 1), which is 3 units away from point A (-1, -2) and 4 units away from point C (-5, 1). Therefore, the circle with center (-1, -2) and radius 3 would pass through point B, and its equation would be:

(x + 1)2 + (y + 2)² = 3²

(x + 1)2 + (y + 2)² = 9

The solution for x in the equation (x – 7)^2 = 36 are x = 13 and x = 1

We can solve for x by taking the square root of both sides of the equation:

(x – 7)^2 = 36

Taking the square root of both sides:

x - 7 = ±6

Adding 7 to both sides:

x = 7 ± 6

Therefore, the values of x are:

x = 7 + 6 = 13

x = 7 - 6 = 1

So the correct answers are x = 13 and x = 1. The values x = -29 and x = 42 are not solutions to the equation.

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The conditional value probability is solved and P ( J ) = 0.1105

Given data ,

P(JIK) = 0.35, P(KJ) = 0.95, P(K) = 0.3

We can use Bayes' theorem to find P(J):

P(J | K) = P(K | J) * P(J) / P(K)

0.35 = 0.95 * P(J) / 0.3

0.35 * 0.3 = 0.95 * P(J)

0.105 = 0.95 * P(J)

P(J) = 0.105 / 0.95

P(J) = 0.1105

Hence , the probability is P ( J ) = 0.1105

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The accounting equation is:

Assets = Rs. 2,19,500

Liabilities = Rs. 1,000

Capital = Rs. 2,10,500

The accounting equation is:

Assets = Liabilities + Capital

(a) Commenced business with cash of Rs. 1,00,000 and Machine of Rs. 50,000.

Assets = Cash + Machine = Rs. 1,00,000 + Rs. 50,000 = Rs. 1,50,000

(b) Purchased goods for cash Rs. 30,000 and credit Rs. 10,000.

Assets = Cash + Inventory = Rs. 1,30,000

Liabilities = Accounts Payable = Rs. 10,000

(c) Sold goods for cash Rs. 25,000 and credit Rs. 15,000.

Assets = Cash + Accounts Receivable + Inventory = Rs. 1,70,000

Liabilities = Accounts Payable = Rs. 10,000

(d) Goods taken by the owner for private use Rs. 2,000.

Assets = Cash + Accounts Receivable + Inventory - Drawings = Rs. 1,68,000

(e) Cash paid to creditors Rs 8,000.

Assets = Cash + Accounts Receivable + Inventory - Drawings = Rs. 1,60,000

Liabilities = Accounts Payable - Rs. 8,000 = Rs. 2,000

(f) Cash received from debtors Rs. 14,500 in full settlement.

Assets = Cash + Inventory - Drawings = Rs. 1,74,500

Liabilities = Accounts Payable - Rs. 8,000 = Rs. 2,000

Capital = Rs. 1,70,500

(g) Received a loan of Rs. 5,000 from Mr. Dipendra.

Assets = Cash + Inventory - Drawings = Rs. 1,79,500

Liabilities = Accounts Payable - Rs. 8,000 + Loan Payable Rs. 5,000 = Rs. 1,000

Capital = Rs. 1,74,500

(h) He introduced additional capital Rs. 40,000.

Assets = Cash + Inventory - Drawings = Rs. 2,19,500

Liabilities = Accounts Payable - Rs. 8,000 + Loan Payable Rs. 5,000 = Rs. 1,000

Capital = Rs. 2,10,500

Therefore, the accounting equation is:

Assets = Rs. 2,19,500

Liabilities = Rs. 1,000

Capital = Rs. 2,10,500

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Answer:

S = 2π(14^2) + 2π(14)(154)

= 2π(196) + 2π(2,156)

= 4,704π = 14,778.1 ft^2

Using 3.14 for π:

S = 4,704(3.14) = 14,770.6 ft^2

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