domain:1,2,3,4,5 range:68,71,74,77,80 what is a reasonable domain for this

The gross earnings are $225, federal taxes are $40.50, state taxes are $9, social security deduction is $15.86, total deductions are $65.36, and the net pay is $159.64.

The gross earnings are determined by multiplying the pay rate by the number of hours worked.

Federal taxes, state taxes, and social security deductions are calculated by applying the respective tax rates to the gross earnings.

Total deductions are the sum of federal taxes, state taxes, and social security deductions.

Net pay is obtained by subtracting the total deductions from the gross earnings.

To calculate the gross earnings, we multiply the pay rate of $7.50 by the number of hours worked, which is 30.

Therefore, the gross earnings are $7.50 * 30 = $225.

Next, we can calculate the federal taxes by applying the tax rate of 18% to the gross earnings.

The federal taxes amount to 18% * $225 = $40.50.

Similarly, the state taxes can be calculated by applying the tax rate of 4% to the gross earnings.

The state taxes amount to 4% * $225 = $9.

To determine the social security deduction, we apply the tax rate of 7.05% to the gross earnings.

The social security deduction amounts to 7.05% * $225 = $15.86.

The total deductions are the sum of the federal taxes, state taxes, and social security deduction.

Thus, the total deductions are $40.50 + $9 + $15.86 = $65.36.

Finally, to calculate the net pay, we subtract the total deductions from the gross earnings.

Therefore, the net pay is $225 - $65.36 = $159.64.

In conclusion, the gross earnings are $225, federal taxes are $40.50, state taxes are $9, social security deduction is $15.86, total deductions are $65.36, and the net pay is $159.64.

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Answer: A

Step-by-step explanation:

Answer:

A. Add the exponents.

Step-by-step explanation:

The rule for same base multiplication is:

\( a^m \times a^n = a^{m + n} \)

Add the exponents.

Answer: A. Add the exponents.

Answer:

Step-by-step explanation:

isosceles triangle

solve for x:

JK = KL

8x = 13x - 15

15 = 13x - 8x

15 = 5x

x = 3

solve for y:

180 = 76 + 2(5y - 3)

180 - 76 = 10y - 6

10y = 110

y = 11

Answer:

y = -4/3

x = 14/3

Step-by-step explanation:

2x+y=8

x-y=6

First of all, we need the same coefficient, so we can make both of these 2x by multiplying the second one by 2.

2x+y=8

2x-2y=12

Then we need to subtract equation 1 from 2.

3y=-4

Solve normally

y = -1.33333 / -4/3

Substitute

x - (-4/3) = 6

x = 14/3

\(\large\huge\green{\sf{Answer:-}}\)

\( \red {\mathbb{ \underline { \tt by \: elimination \: method \: s}}}\)

from equation (i):-

\(2x - y = 8 \\ x = \frac{8 - y}{2} \)

\(x - y = 6 \\ \frac{8 - y}{2} - y = 6 \\ \frac{8 - y - 2y}{2} = 6 \\ 8 - y - 2y = 12 \\ 8 - 3y = 12 \\ - 3y = 12 - 8 \\ - 3y = 4 \\ y = \frac{ - 4}{3} \)

\(2x + y = 8 \\ 2x + ( \frac{ - 4}{3} ) = 8 \\ 2x - \frac { 4}{3} = 8 \\ \frac{6x - 4}{3} = 8 \\ 6x - 4 = 8 \times 3 \\ 6x - 4 = 24 \\ 6x = 24 + 4 \\ 6x = 28 \\ x = \frac{14}{3} \)

now,

\(2x + y = 8 \\ x - y = 6 \\ - - - - - - - \\ multiply \: eq \: (i) \: by \: 1 \\ and \: eq(ii) \: by \: 2 \\ \\ (2x + y = 8) \times 1\\ (x - y = 6) \times 2 \\ - - - - - - - \\2x + y = 8 \\ 2x - 2y = 12 \\ subtract \: these \\ 3y = - 4 \\ y = \frac{ - 4}{3} \\ \)

put value of y in equation (i)

\(2x + y = 8 \\ 2x + ( \frac{ - 4}{3} ) = 8 \\ 2x - \frac { 4}{3} = 8 \\ \frac{6x - 4}{3} = 8 \\ 6x - 4 = 8 \times 3 \\ 6x - 4 = 24 \\ 6x = 24 + 4 \\ 6x = 28 \\ x = \frac{14}{3} \)

Answer:

x=5

Step-by-step explanation:

2^x=32 , solve for x, so x=5

A) An inequality to represent the temperatures is -40⁰<t<118⁰

B) t∈(-40⁰, 118⁰)

C) The temperature is more than the operating limit and the pilot cannot takeoff.

Inequalities characterize the connection between two non-equal values in mathematics. Inequality means not being equal. In general, if two values are not equal, we use the "not equal sign ()". However, different inequalities are utilized to compare the values, whether it is less than or higher than.

An inequality is a non-equal comparison between two numbers or other mathematical expressions in mathematics. It is most commonly used to compare two numbers on a number line based on their size.

Part A:

Any temperature in that range is safe for the pilot to take off and land in. The disparity can be represented as: -40⁰<t<118⁰

Part B:

The graph is as follows:

Part C :

June 1990, t=122⁰ is over the upper limit of the working temperatures, i.e. it is higher than the maximum operational temperature.

The pilot would not have taken off on that particular day.

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Answer:

bottom left

Step-by-step explanation:

All of the others follow a pattern of addition or subtraction

Answer:

I think the answer would be −329/8 or −41.125 .

Step-by-step explanation:

Hope this helped .

A set of values for the decision variables that satisfy all the constraints and yields the best objective function value is a feasible solution that optimizes the objective function.

In optimization problems, decision variables are the quantities that we can control or adjust to achieve a desired outcome. Constraints are the limitations or conditions that these decision variables must satisfy. The objective function represents the goal or objective we want to optimize.

A feasible solution refers to a set of values for the decision variables that satisfy all the given constraints. This means that the solution meets all the specified requirements and does not violate any constraints. However, there can be multiple feasible solutions that meet the constraints.

Among these feasible solutions, the one that yields the best objective function value is the optimal solution. The objective function value is a measure of how well the solution aligns with the desired objective. The goal is typically to maximize or minimize this objective function value, depending on the problem.

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In the coordinate axis the point D is located at the position of (5,-2) .

In the given graph of the coordinate axis , we can see that the four points A,B,C and D are located

The coordinates of each point are :

A (-5,-2)

B (-2,5)

C (2,-5)

D (5,-2)

Therefore using the given abscissae and ordinate of the points the point that is located at (5,-2) is D.

A coordinate system in geometry is a way to use one or more integers, or coordinates, to determine the exact placement of points or other geometrical objects on a manifold, such Euclidean space.

The order of the coordinates is crucial, and they are frequently identified by their position in an ordered tuple or by a letter, such as "the x-coordinate." The coordinates are often real values in elementary mathematics, but they could also be complex numbers or parts of a more abstract system, such a commutative ring.

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Answer:

Step-by-step explanation:

Use Newton's Law of Cooling here:

\(T(t)=T_s+(T_0-T_s)^{-kt\)

where T(t) is the temp of something after a certain amount of time, t, has gone by; Ts is the surrounding temp, and T0 is the initial temp. k is the constant of cooling. We need to first solve for this using the information given. Filling in what we know:

\(53=35+(73-35)^{-35k\) which can simplify a bit to

\(53=35+(38)^{-35k\) and \(18=38^{-35k\)

Take the natural log of both sides:

\(ln(18)=ln(38)^{-35k\)

Taking the natural log allows us to pull that exponent down out front:

\(ln(18)=-35k*ln(38)\)

and now we can divide both sides by ln(38) to get

-35k = .794585 so

k = -.023

Now that have the value for k, we can go on to solve the rest of the problem which is asking us the temp of the soda after 70 minutes. Filling in using the k value and the new time of 70 minutes:

\(T(t)=35+(38)^{70(-.023)\) and

\(T(t)=35+(38)^{-1.61\) and

\(T(t)=35+.0028612013\) and

T(t) = 35 F, basically the temp of the fridge, which is not surprising!

The equation that will make a system with infinite solutions is the third option.

y = 2x + 6

A system of linear equations will have infinite solutions only if the two equations represent the same line.

Here we know that one of the linear equations of the system is:

2y - 4x = 12

If we now divide the whole equation by 2, we will get:

(2y - 4x)/2 = 12/2

y - 2x = 6

Now we can move the "2x" term to the right side, then we will get.

y = 2x + 6

So the equations:

y = 2x + 6

2y - 4x = 12

Represent the same line, then that system will have infinite solutions.

Finally, the correct option is the third one.

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1) The quantum that should be paid moment for the security is$ 5,634.34. 2) Alicia will have$ in her withdrawal account at age 65.

1) We're given that the security will pay$ 7,000 in 8 times and the interest rate is2.75 per time.

We've to calculate what should be paid moment for the security.

First, we will calculate the present value of the security by using the following formula

PV = FV/( 1 r) n

where, FV = unborn value = $ 7,000

r = periodic interest rate = 2.75

n = number of times = 8

Substituting the given values, we get

PV = $ 7,000/( 10.0275) 8PV = $ 5,634.34

Hence, the quantum that should be paid moment for the security is$ 5,634.34.

2) We're given that Alicia will save$ 6,000 at the end of each time until she's 65.

We need to calculate how important she'll have in her withdrawal account at age 65, given that the account earns6.5 per time.

To calculate the unborn value of her savings, we can use the following formula

FV = PMT *(( 1 r) n- 1)/ r

where, PMT = payment per period = $ 6,000

r = interest rate per period = 6.5 = 0.065

n = number of ages = 40( since she's saving until she's 65 and she's presently 25)

Substituting the given values, we get

FV = $ 6,000 *(( 10.065) 40- 1)/0.065 FV = $

Hence, Alicia will have$ in her withdrawal account at age 65.

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The values of a, b, c are 152°, 28°, 152° respectively.

Angles around a point describes the sum of angles that can be arranged together so that they form a full turn.

The sum of angles at a point will give 360°.

This means that a + b + c + 28 = 360

c +28 = 180° ( angle on a straight line)

c = 180 -28

c = 152°

c = a( alternate angles are equal)

therefore the value of a = 152°

b = 28( alternate angles are equal)

therefore the value of b is 28

therefore the values of a, b, c are 152°, 28°, 152° respectively

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Answer:

Step-by-step explanation:

First you need to graph the two lines.

The solution is the point where the lines intersect.

Answer:

9 > b

Step-by-step explanation:

-13 > 5 - 2b

-13 - 5 > -2b

-18/-2 > b

9 > b

Answer:

Look Below

Step-by-step explanation:

The formula for a circle is πr².

Therefore, we can divide the area of the circle by 3.14, and then square root it. 490.63/3.14=156.25... If you square root that, you get 12.5. Same thing with the other circle. 219.45/3.14=69.888... If you square root that, you get 8.36. Now that we have the radius, we can multiply that by two to find the diameter. And we're done.

Feel free to tell me if I did anything wrong! :)

We will substitute this value of sin²x in our expression which will give;6 tan²x(1 - sin²x)6 tan²x(1 - (1 - cos²x))6 tan²x cos²x.

We need to simplify the given expression which is given below;

6 tan2 x − 6 tan2 x sin2 x

In order to solve this expression, we will first write it in a factored form which will be;

6 tan²x(1 - sin²x)

We know that the identity for sin²x is;sin²x + cos²x = 1

Which can be rearranged to give;

sin²x = 1 - cos²x

Now we will substitute this value of sin²x in our expression which will give;6 tan²x(1 - sin²x)6 tan²x(1 - (1 - cos²x))6 tan²x cos²x.

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the best would be the first choice because it's 7 dollars less than the second choice

Answer:

she saves $24 dollars every month. 36 + 24 =60 +24 =84 +24 =108 +24 =132 :)

Yes, the set S is a basis of R³.Since it is not possible to create a non-trivial linear combination that equals zero, the set S is linearly independent.

For the set S to be a basis of R³, it must be linearly independent and spans R³. Let's test for both these conditions. The set S has 3 vectors, which is the same as the dimension of R³, thus it can span R³. Therefore, we only need to test if it is linearly independent.

Let's set the linear combination of these vectors equal to the zero vector and find values for scalars a, b, and c such that:  a(1, 5, 3) + b(0, 1, 2) + c(0, 0, 6) = (0, 0, 0).This gives us the system of equations:

a = 0, 5a + b

= 0, 3a + 2b + 6c

= 0

Solving for the scalars a, b, and c gives us: a = 0, b = 0, and c = 0.Thus, the only solution for the linear combination is the trivial one. The set S is linearly independent. Therefore, S is a basis of R³.

Thus, yes, the set S is a basis of R³.Since it is not possible to create a non-trivial linear combination that equals zero, the set S is linearly independent. Additionally, because the set S contains three vectors (i.e. the same number as the dimension of R³), it is able to span R³. Thus, it follows that S is a basis of R³.

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Answer: Look at the picture

Step-by-step explanation: Hope this help :D

The global minimum of a function is the point where the function reaches its lowest value. To find this point for the rate of change of air temperature (dH/dt) as a function of time (t), we can analyze the given data. Global minimum for this functionis 6:00. The correct answer is option e

\(t (hours since midnight): 5, 6, 7, 8, 9dH/dt (°F/hour): -5, -10, 24\)

From the data, we can see that the rate of change is negative at 5:00 (dH/dt = -5) and 6:00 (dH/dt = -10), which means the air temperature is decreasing during these hours. At 7:00, the rate of change becomes positive (dH/dt = 24), indicating that the air temperature is now increasing.

The global minimum for this function occurs when the rate of change transitions from negative to positive, as it represents the point where the air temperature stops decreasing and starts increasing. In this case, the global minimum occurs at 6:00 (t = 6), as it is the last time when the rate of change is negative before becoming positive.

So, the correct answer is e. 6:00. The correct answer is option e

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Answer:

The last two digits of 6²⁰²⁰ + 7²⁰²⁰ is 7, 7

Step-by-step explanation:

The given question is to find the value of the sum of two numbers 6²⁰²⁰ + 7²⁰²⁰, where,  6²⁰²⁰ + 7²⁰²⁰ ≠ 13²⁰²⁰

We have;

The last two digits of the powers of 6 are;

6¹ = 6, last two digits = 06

6² = 36, last two digits = 36

6³ = 216, last two digits = 16

6⁴ = 1,296, last two digits = 96

6⁵ = 7,776, last two digits = 76

6⁶ = 46,456, last two digits = 56

6⁷ = 279,936, last two digits = 36

6⁸ = 1,679,616, last two digits = 16

6⁹ = 10,077,696, last two digits = 96

6¹⁰ = 60,466,176, last two digits = 76

6¹¹ = 362,767,056, last two digits = 56

Therefore, the last two digits repeat itself every 5 times

For 6²⁰²⁰, the last two digits will be for the 2020/5 = 404 complete times, which will be 76

The last two digits of the powers of 7 are;

7¹ = 7, last two digits = 07

7² = 49, last two digits = 49

7³ = 343, last two digits = 43

7⁴ = 2,401, last two digits = 01

7⁵ = 16,807, last two digits = 07

7⁶ = 117,649, last two digits = 49

7⁷ = 823,543, last two digits = 43

7⁸ = 5,764,801, last two digits = 01

Therefore, the last two digits repeat itself every 4 times

For 7²⁰²⁰, the last two digits will be for the 2020/4 = 505 complete times, which will be 01

Therefore, the last two digits of 6²⁰²⁰ + 7²⁰²⁰ is 76 + 01 = 77, which is 7, 7

The slope of the tangent line to the graph of f(x) = −x² + 4x at x = 4 is 0, and the equation of the tangent line is y = 0.

The slope of a tangent line to a graph of a function is a measure of how steeply the function is increasing or decreasing at a certain point. A tangent line is a line that just touches the graph at a single point and has the same slope as the graph at that point.

Here we need to find the slope of the tangent line to the graph of

=> f(x) = −x² + 4x at x = 4,

we first need to determine the derivative of the function. The derivative of the function gives us the rate of change of the function, which is the slope of the tangent line.

Here The derivative of f(x) = −x² + 4x is given by

=> f'(x) = −2x + 4.

Now we have to find the slope of the tangent line at x = 4, we evaluate the derivative at x = 4:

=> f'(4) = −2 * 4 + 4 = 0.

So, the slope of the tangent line at x = 4 is 0.

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The amount of alcohol remaining after 4 hours would be approximately 64 mg/dL.

We can use the formula for exponential decay to model the amount of alcohol remaining in the blood after t hours:

\(Q(t) = Q_o* e^{(-kt)\)

where Q₀ is the initial amount of alcohol in the blood, k is the decay constant, and t is the time elapsed.

We know that Q₀ = 200 mg/dL, and Q(2) = 128 mg/dL. We can use this information to solve for k:

\(128 = 200 * e^{(-k*2)\)

\(e^{(2k)} = 200/128\)

2k ≈ ln(1.5625)

k ≈ -0.345

Now we can use this value of k to find Q(4):

\(Q(4) = 200 * e^{(-0.345*4)\)

Q(4) ≈ 64

Therefore, the amount of alcohol is 64 mg/dL.

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Answer:

22/7 is not pi

Step-by-step explanation:

22/7 is just a close approximation for pi, not pi itself.

If you put 22/7 into a calculator, you get:

3.142857...

While the number pi itself is:

3.1415926...

You can notice that pi is actually different than 22/7, even though the two numbers start out the same and are close to each other. Frequently in geometry, you use 22/7 as pi because it's so close and makes calculation easier.

Hope this helps!

Answer:

none. they have already sold exactly $400,000 worth of computers and accessories