Question 15 of 25
The table below shows last year's gross income, standard deduction, and
number of exemptions for four different workers.
Gross
Income
Delaney $77,568
Jamie $71,234
Oliver $74,872
Thomas $77,623
Standard
Deduction
$8350
$5700
$8350
$5700
2
1
1
3
Number of Exemptions at
$3650 Each
Assuming that each worker used the standard deduction and that none of the
workers had any additional adjustments, which worker had the lowest taxable
income last year?

Answer:

A

Step-by-step explanation:

Concept :-

On converting :-

\(\bf\implies y + 5 =\dfrac{1}{3}(x-9)\\\\\bf\implies y + 5 =\dfrac{1}{3}x - 3 \\\\\bf\implies y = \dfrac{1}{3}x - 3 - 5 \\\\\bf\implies\boxed{\red{y = \dfrac{1}{3}x -8 }}\)

a. The probability that you win on none of your 5 plays is approximately 0.6634. b. The probability that you win 3 or more of your 5 plays of this game is approximately 0.004497.

To solve these problems, we'll use the binomial probability formula.

a. The probability of winning in any one play is 0.08, so the probability of losing in any one play is 1 - 0.08 = 0.92.

The probability of winning on none of your 5 plays can be calculated as the probability of losing on each play, which is 0.92, raised to the power of the number of plays.

P(losing all 5 plays) = (0.92)^5 = 0.6634 (rounded to four decimal places)

Therefore, the probability that you win on none of your 5 plays is approximately 0.6634.

b. To find the probability of winning 3 or more of your 5 plays, we need to calculate the probability of winning 3, 4, or 5 plays and sum them up.

P(winning 3 or more plays) = P(winning 3 plays) + P(winning 4 plays) + P(winning all 5 plays)

P(winning 3 plays) = C(5, 3) *\((0.08)^3 * (0.92)^2\)

                  = 10 * 0.000512 * 0.8464

                  ≈ 0.00434 (rounded to five decimal places)

P(winning 4 plays) = \(C(5, 4) * (0.08)^4 * (0.92)^1\)

                  = 5 * 0.000032768 * 0.92

                  ≈ 0.000151 (rounded to six decimal places)

P(winning all 5 plays) = \((0.08)^5\)

                     ≈ 0.000006 (rounded to six decimal places)

Now we can sum up these probabilities:

P(winning 3 or more plays) ≈ 0.00434 + 0.000151 + 0.000006

                          ≈ 0.004497 (rounded to six decimal places)

Therefore, the probability that you win 3 or more of your 5 plays of this game is approximately 0.004497.

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Answer:

(-3/2, -13/2)

Step-by-step explanation:

To solve the system of equations graphically, we need to plot the two equations on the same set of axes and find the point of intersection.

To plot the first equation y = x - 5, we can start by finding the y-intercept, which is -5. Then, we can use the slope of 1 (since the coefficient of x is 1) to find other points on the line. For example, if we move one unit to the right (in the positive x direction), we will move one unit up (in the positive y direction) and get the point (1, -4). Similarly, if we move two units to the left (in the negative x direction), we will move two units down (in the negative y direction) and get the point (-2, -7). We can plot these points and connect them with a straight line to get the graph of the first equation.

To plot the second equation y = -x - 8, we can follow a similar process. The y-intercept is -8, and the slope is -1 (since the coefficient of x is -1). If we move one unit to the right, we will move one unit down and get the point (1, -9). If we move two units to the left, we will move two units up and get the point (-2, -6). We can plot these points and connect them with a straight line to get the graph of the second equation.

The point of intersection of these two lines is the solution to the system of equations. We can estimate the coordinates of this point by looking at the graph, or we can use algebraic methods to find the exact solution. One way to do this is to set the two equations equal to each other and solve for x:

x - 5 = -x - 8 2x = -3 x = -3/2

Then, we can plug this value of x into either equation to find the corresponding value of y:

y = (-3/2) - 5 y = -13/2

So the solution to the system of equations is (-3/2, -13/2).

In this problem set, we will be solving three different equations involving trigonometric functions. Within the interval 0 ≤ t < 2π, the solutions are t = π/6 and t = 11π/6. Within the interval 0 ≤ t < 2π, the solutions are t = π/3 and t = 5π/3. And for the third equation, there is no solution.

When solving these equations, we will be looking for all radian solutions, as well as solutions within the interval 0 ≤ t < 2π.

It's important to remember that an equation is simply a mathematical statement that shows that two expressions are equal. In order to solve the equation, we need to manipulate the expressions in such a way that we can isolate the variable we are solving for.

For the first equation, we are given 9 cos t - root3 = 7 cos t. To solve for t, we want to isolate the cosine term on one side of the equation. We can do this by subtracting 7 cos t from both sides, which gives us 2 cos t - root3 = 0. Next, we can divide both sides by 2 to get cos t = root3/2. We recognize that this is a special angle for cosine, which occurs at π/6 and 11π/6 radians. Therefore, the solutions for all radian values of t are t = π/6 + 2kπ and t = 11π/6 + 2kπ, where k is any integer. Within the interval 0 ≤ t < 2π, the solutions are t = π/6 and t = 11π/6.

For the second equation, we have 3 cos t = 9 cos t - 3 root3. Similar to the first equation, we want to isolate the cosine term on one side, so we can subtract 9 cos t from both sides, which gives us -6 cos t = -3 root3. Dividing both sides by -6, we get cos t = 1/2 root3. Again, this is a special angle for cosine, which occurs at π/3 and 5π/3 radians. Therefore, the solutions for all radian values of t are t = π/3 + 2kπ and t = 5π/3 + 2kπ, where k is any integer. Within the interval 0 ≤ t < 2π, the solutions are t = π/3 and t = 5π/3.

For the third equation, we have 5 sin t + 8 = -3 sin t. To isolate the sine term, we can add 3 sin t to both sides, which gives us 8 = -2 sin t. Dividing both sides by -2, we get sin t = -4. This is not a valid solution, as the range of the sine function is between -1 and 1. Therefore, there is no solution to this equation.

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Answer:

x≥3

Step-by-step explanation:

7x-28≥-7

Add 28 to each side

7x-28+28≥-7+28

7x≥21

Divide by 7

7x/7≥21/7

x≥3

Answer:

7x-28≥-7

7x≥21

x≥3

To find an exponential regression equation for the given set of data, we need to express it in the form of y = ab^x, where a represents the initial value of the car and b represents the growth or decay factor.

Using the provided data, we can form the following table:

Years (x) Value in dollars (y)

0 15600

1 14254

2 12189

3 10822

4 9618

5 7994

6 6686

To find the exponential regression equation, we can use statistical software or calculators that provide regression analysis. Using these tools, we can obtain an equation in the form of y = ab^x. Let's assume the equation is:  y = 15600 * (0.91)^x

Rounding the coefficient to the nearest hundredth, we get: y = 15600 * (0.91)^x

To determine the value of the car after 15 years, we substitute x = 15 into the equation: y = 15600 * (0.91)^15

Evaluating the expression gives us the value of the car after 15 years.

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Answer:

Step-by-step explanation:

Take the root of both sides and solve.

Exact Form:  v = 2 √ 11 − 3 ,  − 2 √ 11 − 3

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a). We have proved all the given conditions.

b). It is true that condition 3 holds for all regular languages L1 and L2.

(a) Regular languages L1 and L2 can be suggested as follows:

Let \(L_1={0^{(n+1)} | n\geq 0}\)

and

\(L_2={1^{(n+1)} | n\geq 0}\)

We have to prove three conditions:1. L1 ⊈ L2:

The given languages L1 and L2 both are regular but L1 does not contain any string that starts with 1.

Therefore, L1 and L2 are distinct.2. L2  L1:

The given languages L1 and L2 both are regular but L2 does not contain any string that starts with 0.

Therefore, L2 and L1 are distinct.3. (L1 ∪ L2)* = L1* ∪ L2*:

For proving this condition, we need to prove two things:

First, we need to prove that (L1 ∪ L2)* ⊆ L1* ∪ L2*.

It is clear that every string in L1* or L2* belongs to (L1 ∪ L2)*.

Thus, we have L1* ⊆ (L1 ∪ L2)* and L2* ⊆ (L1 ∪ L2)*.

Therefore, L1* ∪ L2* ⊆ (L1 ∪ L2)*.

Second, we need to prove that L1* ∪ L2* ⊆ (L1 ∪ L2)*.

Every string that belongs to L1* or L2* also belongs to (L1 ∪ L2)*.

Thus, we have L1* ∪ L2* ⊆ (L1 ∪ L2)*.

Therefore, (L1 ∪ L2)* = L1* ∪ L2*.

Therefore, we have proved all the given conditions.

(b)It is true that condition 3 holds for all regular languages L1 and L2.

This can be proved by using the fact that the union of regular languages is also a regular language and the Kleene star of a regular language is also a regular language.

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Answer:

2232.48 meters

Step-by-step explanation:

From the diagram:

Radius of semicircle = 74

Length of straightway on each side = 1000

The length of school track :

Straightway on each side = 2 * 1000 m = 2000m

Length of semicircle = πr/2

Length of both semicircle  = 2 * 3.142 * 74 /2 = 232.47785

Total Length = ( 2000 + 232.47785) = 2232.48 meters

☺ I might have misunderstood, but I can help if you give me the question. ☺

Answer:

lateral Surface Area(LSA)=2×22/7×4.9(4.9+11.2)

LSA=2×22/7×4.9×16.1

LSA=495.88

The nearest whole number is 496

Answer: D

Step-by-step explanation:

I think it’s D I’m not sure

Answer: The first one, y = 3x - 4

Hope this helps :)

Answer:

Option 1, which is y= 3x - 4

Answer:

2^x = 2*2*2*2*2

2^X = 2^5

x=5

Step-by-step explanation:

Answer:

5.5

Step-by-step explanation:

2x+7=16

   -7   -7

2x=11

2x/2=11/2

x=5.5

The value of \($\cos \frac{7\pi}{12} \cos \frac{\pi}{12} - \sin \frac{7\pi}{12} \sin \frac\pi{12}$\) is 0.

What is trigonometric identity?

A trigonometric identity is an equation that relates different trigonometric functions of an angle or combination of angles. These identities are true for all possible values of the angles involved. Trigonometric identities are fundamental tools in solving problems involving angles and in simplifying expressions involving trigonometric functions.

We can use the trigonometric identity \($\cos(\alpha-\beta)=\cos\alpha\cos\beta+\sin\alpha\sin\beta$\) to simplify the given expression:

\($\cos\frac{7\pi}{12}\cos\frac{\pi}{12}-\sin\frac{7\pi}{12}\sin\frac{\pi}{12} &= \cos\left(\frac{7\pi}{12}-\frac{\pi}{12}\right) $\)

\($= \cos\frac{6\pi}{12} $\)

\($= \cos\frac{\pi}{2} $\)

\($= \boxed{0}.$\)

Therefore, the value of \($\cos \frac{7\pi}{12} \cos \frac{\pi}{12} - \sin \frac{7\pi}{12} \sin \frac\pi{12}$\) is 0.

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However, we need to substitute a with s since that is the value we have calculated. Therefore, we get \(A(s) = (1/4)(5 + sqrt(5))s^2.\) This is the function notation that represents the area of a regular pentagon whose perimeter is 140 cm.

Let's consider that s be the length of a side of the regular pentagon.

The perimeter of the regular pentagon will be 5s. Therefore, we have the equation:5s = 140s = 28 cm

Also,

we have the formula for the area of a regular pentagon as:

\($A=\frac{1}{4}(5 +\sqrt{5})a^{2}$,\)

where a is the length of a side of the pentagon.

In order to represent the area of a regular pentagon whose perimeter is 140 cm, we need to substitute a with s, which we have already calculated.

Therefore, we have:\(A(s) = $\frac{1}{{4}(5 +\sqrt{5})s^{2}}$\)

Now, we have successfully used function notation (with the appropriate functions above) to represent the area of a regular pentagon whose perimeter is 140 cm.

The area of a regular pentagon can be represented using function notation (with the appropriate functions above). The first step is to calculate the length of a side of the regular pentagon by dividing the perimeter by 5, since there are 5 sides in a pentagon.

In this case, we are given that the perimeter is 140 cm, so we get 5s = 140, which simplifies to s = 28 cm. We can now use the formula for the area of a regular pentagon, which is\(A = (1/4)(5 + sqrt(5))a^2\), where a is the length of a side of the pentagon.

However, we need to substitute a with s since that is the value we have calculated. Therefore, we get\(A(s) = (1/4)(5 + sqrt(5))s^2.\) This is the function notation that represents the area of a regular pentagon whose perimeter is 140 cm.

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Answer:

The car is going 45 mph

Step-by-step explanation:

Since the speed limit is 35 mph and the car is 10 mph over the speed, we can add them to find out how fast the car is going. We can solve 35+10 which will give us 45. So it is not a sum of 0 but instead a sum of 45.

(hope this helped)

Answer:

35+10 =45

Step-by-step explanation:

add 10 to 35 then divide by 2

Answer:

B

Step-by-step explanation:

"From a table of integrals, we know that for \(\(a \neq 0\)\) and \(\(b \neq 0\):\)

\(\[\int \cos(at) \, dt = \frac{1}{a} \cdot \cos(at) + \frac{1}{b} \cdot \sin(bt) + C\]\)

and

\(\[\int e^a t \cos(bt) \, dt = \frac{e^{at}}{a} \cdot \cos(bt) + \frac{b}{a^2 + b^2} \cdot \sin(bt) + C\]\)

Use this antiderivative to compute the following improper integral:

\(\[\int_{-\infty}^{0} \cos(3t) \, dt = \lim_{{T \to \infty}} \int_{0}^{T} e^t \cos(3t) \, e^{-st} \, dt = \lim_{{T \to \infty}} \text{ if } s \neq 1, \, \text{ or } \lim_{{T \to \infty}} \text{ if } s = 1.\]\)

For which values of \(\(s\)\) do the limits above exist? In other words, what is the domain of the Laplace transform of \(\(\frac{1}{\cos(3)} \cdot e^t \cos(3t)\)\)?

Evaluate the existing limit to compute the Laplace transform of  on the domain you determined in the previous part:

\(\[L\{e^t \cos(3t)\\).

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Answer:

Hello

Step-by-step explanation:

Answer:

LES GOOO

Step-by-step explanation:

thx man

Using Laplace transform to solve for x(t) in

\(x(t) = cos(t) + \int_0^t e^{\lambda-t} x(\lambda) d\lambda\) gives \(X_{int(s)} = X(s) \times (1 / (s - 1)).\)

To solve the given integral equation using the Laplace transform, we first take the Laplace transform of both sides of the equation.

Let X(s) be the Laplace transform of x(t), where s is the complex frequency variable. The Laplace transform of x(t) is defined as X(s) = L{x(t)}.

Taking the Laplace transform of the given equation, we have:

\(L{x(t)} = L{cos(t)} + L{\int_0^t e^{\lambda-t} x(\lambda) d\lambda}\)

Using the linearity property of the Laplace transform, we can split the equation into two parts:

\(X(s) = X_{cos(s)} + X_{int(s)},\)

where \(X_{cos(s)}\) is the Laplace transform of cos(t) and \(X_{int(s)}\) is the Laplace transform of the integral term.

The Laplace transform of cos(t) is given by:

Lcos(t) = s / (s² + 1).

For the integral term, we can use the convolution property of the Laplace transform. Let's denote X(s) = L{x(t)} and \(X_{int(s)} = L{\int_0^t e^{\lambda-t} x(\lambda) d\lambda}\) . Then, the convolution property states that:

\(L{\int_0^t e^{\lambda-t} x(\lambda) d\lambda} = X(s) * L{e^{\lambda - t}},\)

where * denotes convolution.

The Laplace transform of \(e^{\lambda - t}\) is given by:

\(L{e^{\lambda - t}} = 1 / (s - 1).\)

Therefore, we have: \(X_{int(s)} = X(s) \times (1 / (s - 1)).\)

To solve for X(s), we can substitute these results back into the equation \(X(s) = X_{cos(s)} + X_{int(s)}\)and solve for X(s). Finally, we can take the inverse Laplace transform of X(s) to obtain the solution x(t) to the integral equation.

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Complete Question:

Use Laplace transform to solve for x(t) in

\(x(t) = cos(t) + \int_0^t e^{\lambda-t} x(\lambda) d\lambda\)

Answer:

Its c

Step-by-step explanation:

a) The net price of the products is $653.99. b) The rate of the discount on the products is approximately 15.00%.

a) The net price of the products can be calculated by subtracting the trade discount from the list price. In this case, the list price is $769.40 and the trade discount is $115.41.

Net price = List price - Trade discount

Net price = $769.40 - $115.41

Net price = $653.99

Therefore, the net price of the products is $653.99.

b) The rate of the discount on the products can be determined by dividing the trade discount by the list price and multiplying by 100 to get the percentage. In this case, the trade discount is $115.41 and the list price is $769.40.

Discount rate = (Trade discount / List price) * 100

Discount rate = ($115.41 / $769.40) * 100

Discount rate = 0.149999 * 100

Discount rate = 14.9999%

Therefore, the rate of the discount on the products is approximately 15.00%.

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The measure of angle AOC is 30 degrees. Angle AOC is classified as an acute angle.

An angle that has a measure that is less than 90 degrees is classified as an acute angle.

Given the diagram below, the angle that is formed by rays AO and CO is angle AOC. The instrument shows that angle AOC is exactly 30 degrees.

30 degrees is less than 90 degrees and can therefore be termed an acute angle.

Therefore, the measure of angle AOC is 30 degrees. Angle AOC is classified as an acute angle.

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Answer:

(-4,2) (0,5) (4,8)

Step-by-step explanation:

Answer:

slope= 3/4, y-intercept= (0,5)

Step-by-step explanation:

I don't really know how to explain this but I'll try my best

points are (5,0), (-4,2), and (4,8)

connect all of these points to create the line

Answer:

answer is A

Step-by-step explanation:

The answer is A

Answer:

-300

Step-by-step explanation:

Step 1:  Find the amount Elmer's funds decreased after purchasing the rabbits:

Let x represent Elmer's funds.

Since Elmer bought five rabbits for $10 each, he lost $10 5 times.

x - (10 * 5)

x - 50

Thus, Elmer lost (spent) $50 for the 5 rabbits.

Step 2:  Find the amount Elmer's funds decreased after purchasing the  cupboards:

Since Elmer bought four cupboards for $70 each, he lost $70 4 times:

x - (50 + (70 * 4))

x - (50 + 280)

x - 330

Thus, after purchasing the rabbits and cupboards, Elmer lost $330.

Step 3:  Find the amount Elmer's funds increased after finding the twenty-dollar bill:

Since Elmer found a twenty-dollar bill, he gained $20

x - (330 + 20)

x - 310

Step 4:  Find the amount Elmer's funds increased after returning one rabbit:

Since Elmer returned one rabbit, he gained $10:

x - (310 + 10)

x - 300

Thus, Elmer's funds changed totally by -$300.

Putting all the information together, we have:

x - 10 - 10 - 10 - 10 - 10 - 70 - 70 - 70 - 70 + 20 + 10

x - 50 - 280 + 30

x - 330 + 30

x - $300

Answer:

  (a)  0.0062

Step-by-step explanation:

You want the probability P(X > 14.5) given that X has a normal distribution with mean 2 and variance 25.

This probability can be found using a suitable calculator or spreadsheet. The calculator in the attachment specifies the normal distribution using mean and standard deviation, so we need to find the square root of the variance.

  P(X > 14.4) ≈ 0.0062

<95141404393>

Since it's an arithmetic sequence,

\(a_2 = a_1 + d\)

\(a_3 = a_2 + d = a_1 + 2d\)

\(a_4 = a_3 + d = a_1 + 3d\)

and so on, up to

\(a_n = a_1 + (n-1)d\)

Now, by substitution,

\(a_1 + a_3 + a_5 = -12\)

\(a_1 + (a_1+2d) + (a_1+4d) = -12\)

\(3a_1 + 6d = -12\)

\(a_1 + 2d = -4\)

\(\implies a_1 = -4-2d, a_3 = -4, a_5 = -4+2d\)

Then the product \(a_1a_3a_5=80\) depends only on d, so that

\((-4-2d) \times (-4) \times (-4+2d) = 80\)

Solve for d :

\((4+2d) (4-2d) = -20\)

\(16 - 4d^2 = -20\)

\(4d^2 = 36\)

\(d^2 = 9\)

\(d = \pm3\)

If d = 3, then the first term in the sequence is \(a_1 = -10\), and the tenth term would be \(a_{10} = \boxed{17}\).

If d = -3, then the first term would instead by \(a_1 = 2\), and the tenth term would be \(a_{10} = \boxed{-25}\).