Heather takes a 15 question exam. If she has an 87% chance to pick the correct answer, what is the probability of her getting exactly 12 out of 15 correct? Round your answer to two decimal places.
Provide your answer below:

[2x^(2) + 7x + 6 = 0] has C. two real solutions

The quadratic equation 2[tex]x^{(2)}[/tex] + 7x + 6 = 0 has two real solutions. To solve, use the Quadratic Formula:

x = [-b ± √([tex]b^{2}[/tex] - 4ac)]/2a  

Where a = 2, b = 7, and c = 6.

So, x = [-7 ± √([tex]7^{2}[/tex]- 4(2)(6))]/2(2)  

x = [-7 ± √(49 - 48)]/4  

x = [-7 ± 1]/4  

x = -3/2 and x = 1/2  


Therefore, the equation has two real solutions: x = -3/2 and x = 1/2.

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The result of the given polynomial division (2x^(3)+4x^(2)+7x+5 divided by x+1) using long division method is 2x^(2) + 2x + 5.

To find the result of the given polynomial division using long division method, we need to follow the steps below:

Step 1: Write the dividend and the divisor in long division form.

        ______________________
x + 1  |  2x^(3) + 4x^(2) + 7x + 5

Step 2: Divide the first term of the dividend by the first term of the divisor. In this case, 2x^(3)/x = 2x^(2). Write the result above the dividend.

        2x^(2)  _______________
x + 1  |  2x^(3) + 4x^(2) + 7x + 5

Step 3: Multiply the result by the divisor and write the product under the dividend.

        2x^(2)  _______________
x + 1  |  2x^(3) + 4x^(2) + 7x + 5
        - (2x^(3) + 2x^(2))
        ---------------------

Step 4: Subtract the product from the dividend and bring down the next term.

        2x^(2)  _______________
x + 1  |  2x^(3) + 4x^(2) + 7x + 5
        - (2x^(3) + 2x^(2))
        ---------------------
                2x^(2) + 7x + 5

Step 5: Repeat the process until the degree of the remainder is less than the degree of the divisor.

        2x^(2) + 2x + 5  _______________
x + 1  |  2x^(3) + 4x^(2) + 7x + 5
        - (2x^(3) + 2x^(2))
        ---------------------
                2x^(2) + 7x + 5
        - (2x^(2) + 2x)
        ---------------------
                   5x + 5
        - (5x + 5)
        ---------------------
                   0

Step 6: Write the final result as the quotient plus the remainder over the divisor.

[tex](2x^{3} + 4x^{2} + 7x + 5)/(x + 1) = 2x^{2} + 2x + 5[/tex]

Therefore, the answer is 2x^(2) + 2x + 5

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Answer:

112m

Step-by-step explanation:

The area of the given  Parallelogram is 112 m².

given that the parallelogram in fig.. We splits this parallelogram in three parts, that is, first is triangle ,second is square and third is again a triangle.

Since, the area of triangle:

[tex]\mathrm{Area\ of\ triangle}=\frac{1}{2}[/tex] × base × height

and the [tex]\mathrm {Area\ of\ Square}=[/tex] width × height.

Here in triangle, base=6 and height=8

[tex]\mathrm {Area\ of\ Square}=[/tex]

therefor the [tex]\mathrm{Area\ of\ triangle}=\frac{1}{2}[/tex]×6×8

                                               =24m².

Here in square,  width=8 and height=8

therefore the [tex]\mathrm {Area\ of\ Square}=[/tex] 8×8

                                               =64m².

Area of first split, that is, triangle is 24 m².

Area of second split, that is, square is 64 m².

Area of third split, that is, again a triangle is 24 m².

Total area= 24+64+24

                 =112 m².

Therefor the total area of parallelogram is 112 m².

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Answer:

Assuming that the final exam is worth 20% of the final grade, we can use the following formula to calculate the overall grade:

overall grade = (0.8 * current grade) + (0.2 * final exam grade)

Plugging in the values given in the problem, we get:

overall grade = (0.8 * 77%) + (0.2 * 0%) = 61.6%

Therefore, if you get a score of 0/20 on the final exam, your overall grade would be 61.6%.

Conduct a hypothesis test or calculate and compare the measures of center and spread for each sample.to determine if there is a statistically significant difference between the two waiting line configurations.

1. We can use a two-sample t-test to compare the means of the two samples and determine if the difference is statistically significant. The null hypothesis would be that there is no difference between the means of the two samples, and the alternative hypothesis would be that there is a significant difference between the means.

If the p-value is less than the significance level (e.g., 0.05), we can reject the null hypothesis and conclude that there is a statistically significant difference between the waiting times for the two configurations.

2. The two samples of waiting times from the hospital experiment can be compared by using the measures of center, such as the mean and median, and the measures of spread, such as the standard deviation and range.

In conclusion, to compare the two samples from the hospital experiment, conduct a hypothesis test or calculate and compare the measures of center and spread for each sample.

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The formula for the delta-loss operator and the delta-gamma loss operator if the risk factor changes are chosen to be the log returns of S is ΔΓL = (1/2) * CBS * (tn - ln(Sn/Sn-1))².

The delta-loss operator is given by the formula: ΔL = CBS * (tn - Sn). This represents the change in loss for a given change in the underlying risk factor, S.

The delta-gamma loss operator is given by the formula: ΔΓL = (1/2) * CBS * (tn - Sn)²s represents the change in loss for a given change in the underlying risk factor, S, and also takes into account the curvature of the loss function.

To find the formula for the delta-loss operator and the delta-gamma loss operator if the risk factor changes are chosen to be the log returns of S, we can simply substitute the log returns of S for the risk factor changes in the formulas above. The log returns of S are given by the formula: ln(Sn/Sn-1).

So, the formula for the delta-loss operator with log returns of S is: ΔL = CBS * (tn - ln(Sn/Sn-1)). And the formula for the delta-gamma loss operator with log returns of S is: ΔΓL = (1/2) * CBS * (tn - ln(Sn/Sn-1))².

In these formulas, the Greeks C, CBS, and CBS appear as parameters, as requested. These parameters represent the sensitivity of the option value to changes in the underlying risk factor, S.

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After solving the length of BM is 4 cm.

As we know from the question;

AB = 8cm

DL ⊥ AB

BM ⊥ AD

DL = 5cm

AD = 10cm

Think about the parallelogram ABCD now.

Here, let AB be the parallelogram's base and DL be its altitude (height).

The parallelogram's area is determined by: Base × Height

Area of ‖gm ABCD = AB × DL

Area of ‖gm ABCD = 8 × 5

Area of ‖gm ABCD = 40cm²

Now,

Think of AD as the parallelogram's base, and BM as its altitude (height).

area of ‖gm ABCD = AD × BM

10 × BM = 40cm²

Divide by 10 on both side,

BM = 40/10

BM = 4cm

length of BM = 4cm.

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The complete question is:

In ‖gm ABCD, it is given that AB = 8cm, DL ⊥ AB and BM ⊥ AD such that DL = 5cm and AD = 10cm. Then, BM = ?

From function f(x)=x2−3andg(x)=−5x+2,The correct answer is A. (gf​)(52​)= -6.75

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between a variable quantity and another variable quantity.

To find (gf​)(52​), we first need to find f(52​) and then substitute that value into g(x).

First we need to Find f(52​)
f(x)=x2−3
f(52​)=(52​)2−3
f(52​)=52−3
f(52​)=1.75

Then we can  Substitute f(52​) into g(x)
g(x)=−5x+2
g(f(52​))=−5(1.75)+2
g(f(52​))=−8.75+2
g(f(52​))=−6.75

Therefore, (gf​)(52​)=−6.75

The final answer is A. (gf​)(52​)=−6.75

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f (x) = -3x4 + 6x3 + 33x2 - 18x - 108.

The correct answer is a. f (x) = -3x4 + 6x3 + 33x2 - 18x - 108, since this is a polynomial of the lowest degree (4) that has zeros of -2 (multiplicity 2) and 3 (multiplicity 2), as well as f(0)=-108. To solve this problem, use the Factor Theorem to determine the factors of the polynomial. Since the zeros are -2 and 3, the polynomial must factor into (x+2)2 and (x-3)2. This gives us the polynomial: f (x) = -3(x+2)2(x-3)2 - 108. Finally, expand the polynomial to get the answer: f (x) = -3x4 + 6x3 + 33x2 - 18x - 108.

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Answer:

The answer for 17x10^8 is 1,700,000,000 and the answer for 4x10^8 is 400,000,000

subtract them.

Hope that helps you out!

Answer:

3 pages per minuet 90pages/30min=3 pages per min

Step-by-step explanation:

Answer:

3 pages

Step-by-step explanation:

Create a ratio:

30 minutes is equal to 1 hour

90 pages/30 minutes

Divide 90/30

90/30=3

Alya reads 3 pages per minutes

Hope this helped you!

Stay safe and have a good day/night! :)

a) The expected payout for the insurance company is $182.

b) If the insurance company wants to charge 15% over the expected payout, the insurance company should charge the insured $27.30.

In a game of chance, the expected payout is the expected value of the game minus the cost.

For the insurance company, the expected payout is the probability-weighted value of the insurance undertaking.

The expected payout is the product of the amount to be paid to the insured family and the probability or chance of the insured dying.

The amount the insured family will receive = $130,000

The chance of the insured dying = 0.0014

The expected payout = $182 ($130,000 x 0.0014)

Charge over the expected payout = 15%

The amount the insurance company should charge the person = $27.30 ($182 x 15%)

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Answer:30

Step-by-step explanation:

Answer:

Determine the next three terms of each of the number patterns 1 2 4 8 16 32​

1, 2, 4, 8, 16, 32,​ 64, 128, 256

Step-by-step explanation:

You're welcome.

Therefore , the solution of the given problem of probability comes out to be  the likelihood of obtaining a sum of 4 is about 8.3%.

Calculating the likelihood that a claim is true or that a specific event will occur is the primary objective of the branch of mathematics known as parameter estimation. Chance can be represented by any number between 0 and 1, at which 1 usually represents certainty and 0 typically represents possibility. A probability diagram shows the chance that a specific event will occur.

Here,

There are a total of 6 x 6 = 36 results when the spinner is spun twice because there are six sections on it, each with a number from 1 to 6.

We can make a list of every result and determine how many times the sum is 4:

=> 1, 3

=> 2, 2

=> 3, 1

There are three results, and their total is 4. As a result, 3/36 = 1/12 is the chance of receiving a sum of 4. We can multiply this by 100 and tenth it to represent it as a percentage:

=> 1/12 x 100 ≈ 8.3

In other words, the likelihood of obtaining a sum of 4 is about 8.3%.

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The values of the variables are x = 23, y = 41/3, and z = -22/3.

The matrix equation Ax = b for the given set of linear equations is:

```
| -3 0 -6 |   | x |   | 11 |
|  5 -2  3 | * | y | = | 17 |
|  2 -1 -7 |   | z |   | -3 |
```

Where A is the coefficient matrix, x is the column matrix of variables, and b is the column matrix of constants.

To find the inverse of matrix A, we perform row operations on the augmented matrix [A|I]:

```
| -3 0 -6 | 1 0 0 |
|  5 -2  3 | 0 1 0 |
|  2 -1 -7 | 0 0 1 |
```

First, we divide the first row by -3:

```
| 1 0 2 | -1/3 0 0 |
| 5 -2 3 |  0   1 0 |
| 2 -1 7 |  0   0 1 |
```

Then, we subtract 5 times the first row from the second row, and 2 times the first row from the third row:

```
| 1 0  2  | -1/3  0  0 |
| 0 -2 -7 |  5/3  1  0 |
| 0 -1 -3 |  2/3  0  1 |
```

Next, we divide the second row by -2:

```
| 1 0  2  | -1/3  0   0 |
| 0 1 7/2 | -5/6 -1/2 0 |
| 0 -1 -3 |  2/3  0   1 |
```

And then we add the second row to the third row:

```
| 1 0  2  | -1/3  0   0 |
| 0 1 7/2 | -5/6 -1/2 0 |
| 0 0  1/2|  1/6 -1/2 1 |
```

Finally, we divide the third row by 1/2, and subtract 2 times the third row from the first row, and 7/2 times the third row from the second row:

```
| 1 0 0 |  0   1  -2 |
| 0 1 0 | -4/3 2  -7/2|
| 0 0 1 |  1/3 -1  2 |
```

So, the inverse of matrix A is:

```
|  0   1  -2 |
| -4/3 2  -7/2|
|  1/3 -1  2 |
```

Now, we can perform matrix multiplication A^-1b to get the values of the variables:

```
|  0   1  -2 |   | 11 |   | x |
| -4/3 2  -7/2| * | 17 | = | y |
|  1/3 -1  2 |   | -3 |   | z |
```

```
| x |   | 1(17) + (-2)(-3) |   | 23 |
| y | = | (-4/3)(11) + 2(17) + (-7/2)(-3) | = | 41/3 |
| z |   | (1/3)(11) + (-1)(17) + 2(-3) | = | -22/3 |
``

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a.) The value of this vector expression w(u + v) is  

b) The angle between the vectors u and v is  54.73 degrees.

c) the proy uv is -147/25 i + 98/25 j - 196/25 k

a) First we will have to find the sum of the vectors u+v= (3i - 2j + 4k) + (-7i + 4j - 5k) = (-4i + 2j - 1k)

now the dot product of w and (u+v) is

=  (i + j + k). (-4i + 2j - 1k)

= -4+2-1 = -3

b.)

The angle between u and w can be calculated using the dot product: u.w = |u|.|w| cos ∅

u • w = (3i - 2j + 4k) • (i + j + k) = 3 + (-2) + 4 = 5

|u| = √(3² + (-2²) + 4²) = √(25) = 5

|w| = √(1²+ 1² + 1²) = √(3) =3

The angle between u and w can be calculated using the formula: angle ∅ = cos⁻¹(u • w / (|u| • |w|))

angle = cos⁻¹(5 / (5 • √(3))) = cos⁻¹(1/ √3) = 0.6435 radians, or 54.73 degrees.

c.)

To calculate the projection of u onto v, use the formula: proy uv = (u•v/|u|^2) * u

here u.v = (3i - 2j + 4k).(-7i + 4j - 5k)= -49

|u|= 5

proy uv = (-49*(3i - 2j + 4k))/5² = -147/25 i + 98/25 j - 196/25 k

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Answer:

y = -3/2x + 6

Step-by-step explanation:

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

m = (6 - 0)/(0 - 4) = 6/-4 = -3/2

Slope-intercept form is y = mx + b

Substitue m = -3/2, y = 0, x = 4

0 = -3/2(4) + b

b = 6

y = -3/2x + 6

The lateral surface and the total surface areas of the prism are 96 in² and 2304 in² respectively.

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

Given is prism, we need to find the lateral surface and the total surface areas,

Lateral surface area = (perimeter of base) × length

Perimeter of base = 3 × 4 = 12 in

length = 8 in

The lateral surface area = 12 × 8 = 96 in²

Total surface area = (perimeter of base) × length × 2(base area)

= 96 × 2(3×4)

= 96 × 24

= 2304 in²

Hence, the lateral surface and the total surface areas of the prism are 96 in² and 2304 in² respectively.

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The value of 'x' and 'y' in x + 1 : 3y = 1 : 7 and 2x : y + 3 = 2 : 5.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

We know, We can write a : b as, a/b.

Therefore, The given equations can be formed as,

(x + 1)/3y = 1/7 and 2x/(y + 3) = 2/5.

7x + 7 = 3y.

7x - 3y = - 7...(i)

And,

10x = 2y + 6.

10x - 2y = 6...(ii)

Now, Multiplying eqn(i) by 10 and (ii) by 7 we have,

70x - 30y = - 70...(iii) and 70x - 14y = 42...(iv)

Now, By Subtracting (iii) and (iv) we have,

- 16y = - 112

y = 7 and hence x = 2

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The final answer is x ≈ 0.73 radians or x ≈ -0.52 radians.

To solve the trigonometric equation 3Cos2x + Sinx = 1, we will need to use some trigonometric identities and algebraic manipulation. Here are the steps:

Use the double angle identity for cosine to rewrite the equation:
3(1 - 2Sin^2x) + Sinx = 1

Simplify the equation by distributing and rearranging terms:
6Sin^2x - Sinx - 2 = 0

Use the quadratic formula to solve for Sinx:
Sinx = (-(-1) ± √((-1)^2 - 4(6)(-2))) / (2(6))

Simplify the expression:
Sinx = (1 ± √49) / 12

Solve for the two possible values of Sinx:
Sinx = (1 + 7) / 12 = 8/12 = 2/3
Sinx = (1 - 7) / 12 = -6/12 = -1/2

Use the inverse sine function to find the possible values of x in radians:
x = Sin^-1(2/3) ≈ 0.73 radians or x = Sin^-1(-1/2) ≈ -0.52 radians

Check the solutions by plugging them back into the original equation:
3Cos2(0.73) + Sin(0.73) ≈ 1
3Cos2(-0.52) + Sin(-0.52) ≈ 1

Both solutions are valid, so the final answer is x ≈ 0.73 radians or x ≈ -0.52 radians.

Throughout the calculations, we made the assumption that x is in the domain of the trigonometric functions and that the equation has real solutions. We also used the double angle identity for cosine and the quadratic formula to solve the equation.

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The function that describes the profit earned from the sales of the bikes over a period of x years is: [tex]P(x) = 100x^3 + 6x^2 + 9x[/tex]. The Option A is correct.

The profit earned from the sales of the bikes can be calculated by subtracting the cost of manufacturing from the revenue earned. Therefore, the function that describes the profit earned can be represented as:

[tex]P(x) = S(x) - C(x)[/tex]

Substituting the given functions for S(x) and C(x), we get:

[tex]P(x) = (100x^3 + 6x^2 + 97x + 215) - (88x + 215)[/tex]

Simplifying this expression, we get:

[tex]P(x) = 100x^3 + 6x^2 + 9x.[/tex]

Full question "A company sells bikes that are light and fast. The revenue earned over a period of x years can be represented by the function, S(x) = 100x3 + 6x2 + 97x + 215. The cost of manufacturing the bikes can be represented by the function, C(x) = 88x + 215. Which function, P(x), describes the profit earned from the sales of the bikes over a period of x years?"

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Answer:

Let's first convert the time taken to cover the distance at 45 km/h into minutes:

3 hours and 20 minutes = 3 x 60 + 20 = 200 minutes

The distance covered by the bus at 45 km/h is:

distance = speed x time

distance = 45 km/h x 200 minutes

distance = 9000/60 km

distance = 150 km

Now, let's use the distance and the new speed of 36 km/h to calculate the time it would take to cover the same distance:

distance = speed x time

150 km = 36 km/h x time

time = distance / speed

time = 150 km / 36 km/h

time = 4.1667 hours or 4 hours and 10 minutes (rounded to the nearest minute)

Therefore, it would take approximately 4 hours and 10 minutes to cover the same distance at a speed of 36 km/h.

Health club A costs $18 more than health club B charges.

A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x - 2 depicts a linear function because it is a straight line in the coordinate plane.

Any function whose graph is not a straight line is said to be nonlinear. Any curve other than a straight line can be a graph of it.

An example of a non-linear function is a quadratic function.

Given, The equation y = 35x + 40 represents health club B charges.

And the equation for health club A is, 35x + 58.

Now, To obtain how much more health club A charges we have to take the difference which is,

= (35x + 58) - (35x + 40).

= 35x - 35x + 58 - 40.

= $18 more.

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The length of the segment indicated is 10.6.

Pythagoras discovered that the square of the hypotenuse in a right-angled triangle with a 90° angle is equal to the sum of the squares of the other two sides.

The triangle has three sides: the hypotenuse, which is always the longest, the opposite, which doesn't touch the hypotenuse, and the adjacent (which is between the opposite and the hypotenuse).

By Pythagoras' theorem;

a² + b² = c²

a= 16.4

b= 12.5

c =?

16.4² +  12.5² = c²

c² =  268.96 - 156.25 = 112.4

c² = 112.4

c = √112.4

c= 10.6

Therefore, the length of the segment indicated is 10.6.

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Answer:

Step-by-step explanation: the answer is 20, 48, 52

The values of x and y are 100 and 40, respectively

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

The circle

On the circle, we have the following congruent angles

ADC and ABC

Using the above as a guide, we have the following:

x = 100

The sum of angles in a triangle is 180

So, we have

y + y + x = 180

This gives

2y + 100 = 180

So, we have

y = 40

Hence, the value of y is 40

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Answer:

[tex]\large\boxed{\tt (3x+4)(x+7)=3x^{2}+25x+28}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to factor the given trinomial.}[/tex]

[tex]\large\underline{\textsf{What is a Trinomial?}}[/tex]

[tex]\textsf{A Trinomial is an expression that has 3 terms. No more, and no less.}[/tex]

[tex]\large\underline{\textsf{What is Factoring?}}[/tex]

[tex]\textsf{Factoring is a way to split a trinomial into 2 binomials. Binomials have 2 terms.}[/tex]

[tex]\textsf{Factoring helps us to find the possible values of x, setting the binomials equal to 0.}[/tex]

[tex]\textsf{We don't have to do this for our problem though.}[/tex]

[tex]\large\underline{\textsf{Factoring Looks Like;}}[/tex]

[tex]\tt x^{2} + x + 1 = (x+?)(x+?)[/tex]

[tex]\tt The \ 2 x's \ multiply \ to \ equal \ x^{2}.[/tex]

[tex]\textsf{The x's multiply with the whole numbers inside the opposite binomial.}[/tex]

[tex]\large\underline{\textsf{To Factor;}}[/tex]

[tex]\textsf{Factoring is a little tedious, we must be careful and make sure we are finding}[/tex]

[tex]\textsf{the correct factors for factoring to work out. Remember that the trinomial has to}[/tex]

[tex]\textsf{equal the 2 binomials being multiplied.}[/tex]

[tex]\large\underline{\textsf{Solving;}}[/tex]

[tex]\tt 3x^{2} + 25x + 28[/tex]

[tex]\textsf{3x can't be split apart in 2 whole numbers, so it remains 3 in one of the binomials.}[/tex]

[tex]\underline{\textsf{We should have;}}[/tex]

[tex]\tt (3x+?)(x+?)[/tex]

[tex]\textsf{We don't have to worry about} \ \tt 3x^{2} \ \textsf{anymore.}[/tex]

[tex]\textsf{Our goal is to find factors of 28 that multiply to get to 25x and 28.}[/tex]

[tex]\textsf{We might need to try many factor pairs before we have our factored expression.}[/tex]

[tex]\underline{\textsf{Factors of 28;}}[/tex]

[tex]\tt 28: 1, 2, 4, 7, 14, 28.[/tex]

[tex]\textsf{We should substitute the factor pairs in, then FOIL.}[/tex]

[tex]\textsf{Foiling is multiplying 2 binomials together.}[/tex]

[tex]\underline{\textsf{Substitute;}}[/tex]

[tex]\tt (3x+1)(x+28) = 3x^{2}+85x+28[/tex]

[tex]\textsf{Incorrect Factor Pair Whether Flipped or Not.}[/tex]

[tex]\tt (3x+2)(x+14)=3x^{2}+44x+28[/tex]

[tex]\textsf{Incorrect Factor Pair Whether Flipped or Not.}[/tex]

[tex]\large\boxed{\tt (3x+4)(x+7)=3x^{2}+25x+28}[/tex]

[tex]\textsf{Correct Factor Pair. If these factors were flipped it would be incorrect.}[/tex]

Answer:

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Jane deposits $1,250 quarterly into a retirement account that pays interest at the rate of 3.25% per year compounded continuously. At the end of 10 years, she will have $60,358.28 in her account. The correct answer is option 4

To solve the problem, we can use the formula for continuous compounding given by:[tex]A = Pe^{rt}[/tex], where,A is the amount at the end of the investment period, P is the principal (the initial amount deposited), e is Euler's number, which is approximately equal to 2.71828, r is the annual interest rate (expressed as a decimal), t is the time period in years

In this problem, P = $1,250, r = 0.0325 (3.25% as a decimal), and t = 10 years. We need to find A, the amount at the end of 10 years. Substituting the values in the formula, we get:

[tex]A = 1250e^{0.0325 × 10} ≈ $60,358.28.[/tex]

Therefore correct answer is option 4

To know more about Euler's number here:

https://brainly.com/question/30639766

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