Lakisha’s employer pays $2,150 in health insurance and $86 in life insurance per year. She also gets $3,520 in paid time off per year. Her monthly gross pay is $4,370. What are Lakisha’s total job benefits per year? a. $5,756 b. $10,126 c. $52,440 d. $58,196.

He works for 55 hours in order to receive grossly $1,144

From the question, the given parameters are

Hourly rate = $20.80 per hour

Total earnings = $1,144

The number of hours he works for is the quotient of the total earning and the hourly rate

This is represented as

Number of hours =  Total amount /Hourly rate

Substitute the known values in the above equation

So, we have the following equation

Number of hours =  1144/20.8

Evaluate

Number of hours = 55

Hence, the number of hours is 55 hours

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Answer:

Step-by-step explanation:

We know that each backpacks is sold for $40.00.

The goal is to make at least $9,800 per week. With this information we can define the inequality

\(40x -10x \leq 9,800\)

Where \(x\) represents backpacks. Notice that this inequality is about profits, that's why we subtract the cost from the sell price, in this case, the profid margin is $30.00 per backpack, so

\(30x\leq 9,800\)

Solving for \(x\)

\(x\leq \frac{9800}{30}\\ x \leq 326.67\)

Therefore, the factory needs to sell 327 packbacks to make at least 9,800 per week.

Answer:

2.Through a given point not on a line, there exists exactly one line parallel to the given line through the given point.

Step-by-step explanation:

The object of "Euclidean geometry" (more commonly called "plane geometry") is, in principle, the study of the shapes and properties of natural bodies. However, geometry is not an experimental science since its object is not to study certain aspects of nature but a necessarily arbitrary reproduction of it.

After the definitions, Euclid then poses his famous postulates (his requests), the fifth of which has remained Euclid's postulate, often called axiom (or postulate) of parallels and which was the subject of much research and controversy as to its necessity:

From the above explanation, we could deduce that the correct option is Option 2.

Answer:

The answer is B, Through a given point not on a line, there exists exactly one line parallel to the given line through the given point.

Step-by-step explanation:

Answer:

it would be 33 i think

Answer:

x = -7

Step-by-step explanation:

Solve for x:

5 - 4 x + 3 (3 x + 5) = -15

3 (3 x + 5) = 9 x + 15:

(9 x + 15) - 4 x + 5 = -15

Grouping like terms, 9 x - 4 x + 5 + 15 = (-4 x + 9 x) + (5 + 15):

((-4 x + 9 x) + (5 + 15)) = -15

9 x - 4 x = 5 x:

5 x + (5 + 15) = -15

5 + 15 = 20:

5 x + 20 = -15

Subtract 20 from both sides:

5 x + (20 - 20) = -20 - 15

20 - 20 = 0:

5 x = -20 - 15

-20 - 15 = -35:

5 x = -35

Divide both sides of 5 x = -35 by 5:

(5 x)/5 = (-35)/5

5/5 = 1:

x = (-35)/5

The gcd of -35 and 5 is 5, so (-35)/5 = (5 (-7))/(5×1) = 5/5×-7 = -7:

Answer: x = -7

Answer:

x = -7

--------------------------

Hope this helps!

Have a great day and God bless! :)

Answer:

x = 26

y = 9

Step-by-step explanation:

find x first, the 2 angle below have the total of 180 so we have the equation

180 - (5x - 17) = 3x - 11 solve this and you have x = 26

then then opposite angle of 3x - 11 is equal to it and we solve x already so that angle is 67°

we then plus the angle 67° and 2y + 5 we have 90°

so to solve y we have the equation:

67 + (2y + 5) = 90 solve for y and we have y = 9

Answer:

-22

Step-by-step explanation:

given= 0

lost= -8 times 3  =  -24

won= 4    -24+4=-20

lost= -2   -20-2=-22

Answer=-22

Answer: To evaluate the expression 8 7/8 + (7 5/6−2 1/3), you need to start by performing the operation inside the parentheses. The expression inside the parentheses is 7 5/6−2 1/3, which can be rewritten as:

7 + 5/6 - 2 - 1/3

Step-by-step explanation: To add and subtract these fractions, you need to express them with a common denominator. One way to do this is to use a denominator of 6. To express 5/6 with a denominator of 6, you can rewrite it as 5/6 * 1/1 = 5/6. To express 1/3 with a denominator of 6, you can rewrite it as 1/3 * 2/2 = 2/6. When you use these fractions in the expression, you get:

7 + 5/6 - 2 - 2/6

= 7 + 5/6 - 4/6

= 7 - (-1/6)

= 7 + 1/6

= 7 1/6

Now that you have simplified the expression inside the parentheses, you can add 8 7/8 to it:

8 7/8 + (7 1/6)

= 8 + 7/8 + 7 + 1/6

= 15 + 8/8 + 1/6

= 15 + 1 + 1/6

= 16 + 1/6

= 16 1/6

So the final value of the expression is 16 1/6. This fraction is already in simplest form, since the numerator and denominator are relatively prime (i.e., have no common factors other than 1).

After the depression in the principality of Lucastan, the number of unemployed workers who gave up searching completely (3 million) is greater than the number of unemployed workers (8 million).

During the depression, a total of 8 million workers in Lucastan lost their jobs. However, out of these 8 million, only 3 million workers completely gave up searching for employment. This means that there are 3 million workers who are not actively seeking employment anymore.

While both numbers are significant, the 3 million workers who gave up searching completely is greater than the 8 million unemployed workers. This highlights the discouragement and lack of job prospects that led these workers to withdraw from the labor force entirely.

The 3 million workers who have given up searching completely may face challenges in re-entering the workforce, as they may have become discouraged or may have taken on other responsibilities during their period of unemployment. This can have long-term implications for the labor market and the economy of Lucastan.

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the volume of the solid that lies between the paraboloid 2 2 zx y and the sphere 2 22 xyz 2 is (4/15)π.

To find the volume of the solid between the paraboloid and the sphere, we can use cylindrical coordinates. In cylindrical coordinates, the equation of the paraboloid is 2z = r^2 and the equation of the sphere is x^2 + y^2 + z^2 = 2r^2.

We can rewrite the sphere equation as z = (2-r^2)/2 and set it equal to the equation of the paraboloid, giving us:

2r^2 = r^2 + y^2

Simplifying this expression, we get:

y^2 = r^2

This means that the solid lies within the cylinder y^2 + z^2 = 2r^2.

To find the limits of integration, we need to determine the range of r, theta, and z that define the solid. The sphere has a radius of √2, so we know that r must be less than or equal to √2. For theta, we can integrate from 0 to 2π.

To find the limits of integration for z, we need to determine the range of z values for a given r and theta. Substituting r^2/2 for z in the equation of the sphere, we get:

x^2 + y^2 + (r^2/2)^2 = 2r^2

Simplifying this expression, we get:

x^2 + y^2 = (3/4)r^2

This means that for a given r and theta, z can vary from r^2/2 to √(2 - (3/4)r^2).

To find the volume of the solid, we can integrate the function r from 0 to √2, theta from 0 to 2π, and z from r^2/2 to √(2 - (3/4)r^2), using the formula for volume in cylindrical coordinates:

V = ∫∫∫ r dz dr dθ

Evaluating this integral, we get the volume of the solid as (4/15)π.

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Welp ig ur gonna cry bc i SUCK at math xx

When solving proportions, we set the cross products equal, and then we solve for the unknown variable.

When solving proportions, we set the cross products equal to each other and then proceed to solve for the unknown variable. A proportion is an equation that states that two ratios or fractions are equal. To solve a proportion, we first identify the two ratios involved and set their cross-products equal.

For example, consider the proportion: a/b = c/d

To solve for the unknown variable, we set the cross products (a * d) and (b * c) equal:

a * d = b * c

This equation allows us to find the value of the unknown variable by manipulating the equation through multiplication or division to isolate the variable on one side of the equation.

By setting the cross products equal, we essentially establish an equality between the two ratios, indicating that the fractions on either side of the proportion are equivalent. Solving for the unknown variable allows us to determine its value based on the relationship between the given ratios.

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Answer:

4

Step-by-step explanation:

The interest rate at the bank = 2.324 %

Let X be the random variable representing the interest rate on a five-year certificate of deposit (cd) for banks in South Florida in 2018.

Then X follows the Normal Distribution with,

Mean, μ = 2.28 %  and,

Standard Deviation, σ = 0.37 %

We need to find the X at the 45th percentile.

45th percentile implies z-value = 0.45

The z-score at 45th percentile or 0.45 probability = -0.12 [From the z-tables]

We have, z = (x-μ)/σ

⇒ zσ = x-μ

⇒ x = zσ+μ

⇒ x = (0.12 x 0.37) + 2.28

      = 2.324

Hence the interest rate at the bank = 2.324 %

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Answer:

\(V=12\pi\:\text{units}^3\)

Step-by-step explanation:

\(\displaystyle V=\frac{\pi r^2h}{3}\\ \\V=\frac{\pi (3)^2(4)}{3}\\\\V=\pi(3)(4)\\\\V=12\pi\)

There are 30 members in the football squad.

To determine the number of members in the football squad, we can use combinatorics. Since there are 2 positions (captain and assistant captain) to be filled, and the order in which they are chosen does not matter, we can use the formula for combinations. The number of ways to choose 2 people from a group of n is given by n choose 2, which is equal to n(n-1)/2. Therefore, we can set up the equation:

n(n-1)/2 = 930

Solving for n, we get:

n^2 - n - 1860 = 0

Factoring this quadratic equation, we get:

(n - 30)(n + 62) = 0

Since n must be a positive integer, we have:

n = 30

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Answer:

387.02

Step-by-step explanation:

Answer: 387.02

it’s subtraction right

The amount of money that I will have at the end of 20 years would be =$4,480. That is option D

Compound interest is defined as the interest that is being earned on an account which is based on the rate and the time the investment was made.

The total amount invested (p)= $2,000

The rate of investment (r) = 5%

The time of investment(t)= 12 year

The compound interest warm from that account;

= P×T×R/100.

= 2,000×12×5/100

= 120000/100

= $1200

For the next 8 years with the rate of 8% ;

= 2,000×8×8/100

= 128000/100

= $1280

The total compound interest = $1200+$1280= $2,480

Therefore, the amount of money that I will have at the end of 10 years would be = 2000+2480 = $4,480

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On Solving the initial value problem y(t)  , e⁻²¹ dy/dt =y⁻¹(1-e⁻²t); y(0) = 0  , we get the solution is y² = e^(2t) - 2t - 1 .

The function is : e⁻²¹ dy/dt =y⁻¹(1-e⁻²t) ;

⇒ e^(-2t)dy/dt = (1/y)(1-e⁻²t)   ..because y⁻¹ = 1/y ;

⇒ ydy = e^(2t)[1-e^(-2t)) dt ;

⇒ ydy = (e^(2t) - 1)dt ;

now integrating both sides of the problem ;

⇒ y²/2 = [e^(2t)/2 - t]+c ;

Now we know that initial value : y(0) = 0 ;

Substituting y(0)= 0 , we get ;

⇒ 0²/2 = [e⁰/2 - 0]+c ;

⇒ c = -1/2 ;

So , the solution is  y²/2 = [e^(2t)/2 - t] - 1/2 .

it can be written as : y² = e^(2t) - 2t - 1 .

Therefore , the solution of the initial value problem is y² = e^(2t) - 2t - 1 .

Solve the following initial value problems for y(t) by antidifferentiation or by aseparation of variables :  e⁻²¹ dy/dt =y⁻¹(1-e⁻²t); y(0) = 0  .

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Answer: 350

Step-by-step explanation: If you multiply the amount of workers by two, then you divide the amount of time by two, and vice versa. So, in other words, whatever number you multiply the workers by, divide the time by that same number. I hope this helps!

Answer:

p = 16

Step-by-step explanation:

Given p is directly proportional to (q + 2)² then the equation relating them is

p = k(q + 2)² ← k is the constant of proportion

To find k use the condition when q = 1, p = 1

1 = k(1 + 2)² = k × 3² = 9k ( divide both sides by 9 )

\(\frac{1}{9}\) = k

p = \(\frac{1}{9}\) (q + 2)² ← equation of proportion

When q = 10 , then

p = \(\frac{1}{9}\) × (10 + 2)² = \(\frac{1}{9}\) × 12² = \(\frac{1}{9}\) × 144 = 16

It can be concluded that if two lines intersect at right angles, then their direction vectors are necessarily perpendicular or orthogonal. Two vectors are said to be orthogonal if their dot product is zero.

The statement that if two lines intersect at right angles, their direction vectors are necessarily perpendicular is true.

It is always true that when two lines intersect at right angles, they are always perpendicular to each other. In other words, the angle formed between two perpendicular lines is always 90 degrees or a right angle.

Since the dot product between two perpendicular vectors is zero, we can also say that if two lines are perpendicular to each other, then their direction vectors are orthogonal (perpendicular).

Two vectors are said to be orthogonal if their dot product is zero.

Therefore, it can be concluded that if two lines intersect at right angles, then their direction vectors are necessarily perpendicular or orthogonal.

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We need to consider the general problem: \[-(ku')' + cu' + bu = f\]If we discretize by the finite element method with four elements.

On the first and last elements, we use linear shape functions, and on the middle two elements, we use quadratic shape functions. The resulting basis functions are given by:The basis functions ϕ1 and ϕ4 are linear while ϕ2 and ϕ3 are quadratic in nature. These basis functions are such that they follow the property of linearity and quadratic nature on each of the elements.

For the structure of the stiffness matrix K, we need to consider the discrete problem given by \[KU=F\]where U is the vector of nodal values of u, K is the stiffness matrix and F is the load vector. Considering the above equation and assuming constant values of k and c on each of the element we can write\[k_{1}\begin{bmatrix}1 & -1\\-1 & 1\end{bmatrix}+k_{2}\begin{bmatrix}2 & -2 & 1\\-2 & 4 & -2\\1 & -2 & 2\end{bmatrix}+k_{3}\begin{bmatrix}2 & -1\\-1 & 1\end{bmatrix}\]Here, the subscripts denote the element number. As we can observe, the resulting stiffness matrix K is symmetric and has a banded structure.

The element [1 1] and [2 2] are common to two elements while all the other elements are present on a single element only. Hence, we have four elements with five degrees of freedom. Thus, the stiffness matrix will be a 5 x 5 matrix and the structure of K is as follows:

$$\begin{bmatrix}k_{1}+2k_{2}& -k_{2}& & &\\-k_{2}&k_{2}+2k_{3} & -k_{3} & & \\ & -k_{3} & k_{1}+2k_{2}&-k_{2}& \\ & &-k_{2}& k_{2}+2k_{3}&-k_{3}\\ & & & -k_{3} & k_{3}+k_{2}\end{bmatrix}$$Conclusion:In this question, we considered the general problem given by -(ku')' + cu' + bu = f. We discretized it by the finite element method with four elements. On the first and last elements, we used linear shape functions, and on the middle two elements, we used quadratic shape functions. We sketched the resulting basis functions. The structure of the stiffness matrix K was then determined by ignoring boundary conditions. We observed that it is symmetric and has a banded structure.

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The integral defined from 0 to 1 is given by 1/3i.

The integral of the vector-valued function F(t) = (t^2 i + t cos(π) 2 j + sin(π) t k) is to be evaluated over the interval [0,1].

This means we need to integrate each component of the vector-valued function.

We have:

∫F(t) dt = ∫(t^2 i + t cos(π) 2 j + sin(π) t k) dt

= ∫t^2 i dt + ∫t cos(π) 2 j dt + ∫sin(π) t k dt= (1/3) t^3 i + 0 j - (1/π) cos(π) sin(π) t k

= (1/3) t^3 i + 0 j

The answer is (1/3) i

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(a) To classify the origin as an attractor, repeller, or saddle point, we need to look at the eigenvalues of the matrix A. The equation for the discrete dynamical system is xk+1 = Axk, so the Jacobian matrix at the origin is simply A.

The characteristic polynomial of A is given by det(A - λI) = 0, where I is the identity matrix and λ is an eigenvalue. We have:

det(A - λI) = det([1.25-λ 0.75][0.75 1.25-λ]) = (1.25 - λ)(1.25 - λ) - 0.75*0.75 = λ^2 - 2.5λ + 0.5625

Using the quadratic formula, we can solve for the eigenvalues:

λ = (2.5 ± √(2.5^2 - 410.5625)) / 2 = 1.25 ± 0.6614i

Since the eigenvalues have non-zero imaginary parts, the origin is a saddle point.

(b) The directions of the greatest repulsion and greatest attraction are given by the eigenvectors corresponding to the eigenvalues with the largest magnitude. In this case, the eigenvalues with the largest magnitude are 1.25 + 0.6614i and 1.25 - 0.6614i, which have the same magnitude of √(1.25^2 + 0.6614^2) ≈ 1.425. The corresponding eigenvectors are:

[0.75 - (1.25 - 0.6614i)] [0.75 - (1.25 + 0.6614i)]

[0.75] [0.75]

Simplifying, we get:

[0.6614i] [-0.6614i]

[0.75] [0.75]

These eigenvectors represent the directions of the straight line trajectories that experience the greatest repulsion and greatest attraction, respectively. Since the eigenvalues have non-zero imaginary parts, the trajectories will spiral away from or towards the origin.

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Force 2 has a magnitude of approximately 160.8 Newton.

To find the value of force2, we can use the concept of vector equivalence. If force1 has a magnitude of 258 Newton and a length of vector equal to 45 mm, and force2 has a length of vector equal to 28 mm, we can set up the following proportion:

|force1| / length of vector for force1 = |force2| / length of vector for force2

Substituting the given values:

258 / 45 = |force2| / 28

To solve for |force2|, we can cross-multiply and solve for it:

258 * 28 = 45 * |force2|

|force2| = (258 * 28) / 45

Calculating this expression gives us:

|force2| ≈ 160.8 Newton

Therefore, force2 has a magnitude of approximately 160.8 Newton.

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Based on the given information, we can create an inequality to represent the sum of a number (n) and 10 having a maximum value of 120. The inequality can be written as:

n + 10 ≤ 120

To find the possible values of n, we need to isolate n by subtracting 10 from both sides of the inequality:

n ≤ 110

This inequality tells us that the possible values of n are any numbers less than or equal to 110. In other words, n can be any number in the range (-∞, 110], including both negative and positive integers, as well as fractions and decimals. The key takeaway here is that the sum of n and 10 cannot exceed the maximum value of 120, and this constraint is represented by the inequality n ≤ 110.

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The sampling technique used in each study is as follows: (a) convenience sampling, (b) systematic sampling, and (c) stratified random sampling.

(a) In the first study, where a journalist goes to a campground to ask people about their feelings regarding air pollution, the sampling technique used is convenience sampling. This is evident because the journalist approaches individuals who are readily available and easily accessible at the campground. However, convenience sampling may introduce bias as it does not ensure a representative sample of the population.

(b) In the second study, where every tenth machine part is selected from an assembly line for measurement, the sampling technique used is systematic sampling. Systematic sampling involves selecting every nth element from a population after establishing a sampling interval. In this case, every tenth machine part is selected to ensure a systematic and unbiased approach to quality assurance.

(c) In the third study, where attitudes about smoking are studied at a college and students are divided by class and then randomly sampled from each class for interviews, the sampling technique used is stratified random sampling. Stratified random sampling involves dividing the population into homogeneous subgroups (strata) and then randomly selecting samples from each subgroup. By dividing the students into different class strata and randomly selecting samples from each class, this study aims to ensure representation from each class in the final sample.

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The statistics for factory workers is more erratic and has a greater percentage.

The coefficient of variation is an equation that can be used to measure the dispersion of data points in a data set around the mean. It is possible to make the error of counting simply the standard deviation, as I had done in the past.

where mu is the population's mean and sigma represents the population's standard deviation.

Construction workers miss per year is 11.

The standard deviation is 3.1.

Every year, factory workers lose 10 days on average.

The standard deviation of 2.7.

The greatest proportion of CV is thought to be more volatile.

Let's do the math:

Construction workers\(=\frac{\sigma}{\mu} =\frac{3.1}{11}= 0.281*100=28.1\)

Factory workers\(=\frac{\sigma}{\mu}=\frac{2.7}{10}=0.27*100=27\)

Since, the factory workers have a higher percentage, their data is more variable.

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