Damaris owns a small business and is hiring a staff of employees. Each full-time employee
will be paid a yearly salary of $32,000. Each part-time employee will be paid a yearly salary
of $15,000. Damaris has $245,000 allocated for employees' yearly salaries. If Damaris hires
5 part-time employees how many full-time employees can she afford to hire?

Answer:

The Coordinates of Point C are C(5,2)

The slope of CD is 3  

The possible coordinates of point D(a,b) are (6, 5) and (4, -1)  

Step-by-step explanation:

According to the Question,

Now, Let The Coordinates of Point C are C( x , y ) .  

The Coordinates of Point C are C( x , y ) ⇒C(5, 2).  

And, The slope of AB = (1 - 3)/(8 - 2) ⇒ -2/6 ⇔ -1/3 .

Let the coordinate of D be (a, b) then

⇒ √{ (b - 2)² +(a - 5)² } = √10

 on squaring both sides we get,

 ⇒ a² - 10a + 25 + b² - 4b + 4 = 10

 ⇒ a² + b² - 10a - 4b = - 19 ⇔⇔ (Equation 1)  

We Know, the slope of CD = 3

⇒Thus,  (b - 2)/(a - 5) = 3

⇒ b - 2 = 3a - 15

⇒ b = 3a - 13 ⇔⇔ (Equation 2)

Putting value of Equation 2 into Equation 1, We get

⇒a² + (3a - 13)² - 10a - 4(3a - 13) = - 19

⇒a² + 9a² - 78a + 169 - 10a - 12a + 52 = - 19

⇒10a² - 100a + 240 = 0

⇒a² - 10a + 24 = 0

⇒(a - 4)(a - 6) = 0

⇒a = 4 or a = 6

Now,  

When a = 4 , b = 3(4) - 13 ⇒ 12 - 13 ⇒ b = -1

When a = 6, b = 3(6) - 13 ⇒ 18 - 13 ⇒ b = 5

Therefore, the possible coordinates of point D(a,b) are (6, 5) and (4, -1).

Answer:

The answer above is 100% correct

Step-by-step explanation:

I got 100 on my quiz.

Maria can arrange the books on her shelf in (n-2)! ways, where n represents the total number of books excluding the first and last spots.

Since Maria has already decided to place "Pride and Prejudice" in the first spot and "Little Women" in the last spot, the remaining books can be arranged in between these two fixed positions. The number of ways to arrange the books in the remaining spots depends on the total number of books excluding the first and last spots.

Let's say Maria has a total of n books (including "Pride and Prejudice" and "Little Women"). Since these two books are fixed, she needs to arrange the remaining (n-2) books in the remaining spots.

The number of ways to arrange (n-2) books is given by (n-2)!. The factorial (n!) represents the number of ways to arrange n distinct objects.

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Answer:

625

Step-by-step explanation:

I just did this question

Answer:

The sum of the arithmetic series

\(S_{n} = \frac{n}{2} (2 a + (n-1) d)\)

Step-by-step explanation:

Explanation

Let  a , a+d , a+2 d , ..........a+(n-1)d +....... is an arithmetic sequence

The sum of the sequence is called arithmetic series

The \(n^{th}\) term of the sequence

\(t_{n} = a + (n-1) d\)

The sum of the arithmetic series

\(S_{n} = \frac{n}{2} (2 a + (n-1) d)\)

Here 'a' is the first term of the sequence

and 'd' be the difference between two values

sum of first term

put n=1  ⇒  \(S_{1} = a\)

Put n =2 ⇒ \(S_{2} = \frac{2}{2} (2 a + (2-1)d)\)

                  \(S_{2} = 2 a + d\)

......and so on

The sum of the  arithmetic series

\(S_{n} = \frac{n}{2} (2 a + (n-1) d)\)

The check for independence in a one- sample is

The population size is further than 10 times the sample size.

The Correct option is D.

What is Z- test?

A Z- test is a statistical thesis test used to determine whether a sample mean significantly differs from a given population mean when the population standard divagation is known.

For a one- sample z- test for a population proportion, the sample is named without relief from a finite population.

In order for the test to be valid, it's necessary to insure that the sample is small relative to the population size.

still, it can be considered large enough to satisfy the independence supposition, If the population size is further than 10 times the sample size. This supposition is necessary for the validity of statistical conclusion in this environment.

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We can see here that the relationship that exists between the triangular numbers and the rectangular numbers​ is that a doubling of the triangular number will give the rectangular number.

When dots or other items are placed in the form of a triangle, a triangular number is one that may create an equilateral triangle. It is a run of numbers that adheres to a particular pattern.

Beginning with 1, the series of triangular numbers continues by adding subsequent positive integers. The total of all positive integers up to a specific number makes up each triangular number.

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77.5d + .14m

m = 425

.14 * 425 = 59.5

77.5d + 59.5 ≤ 230

77.5d ≤ 170.5

d ≤ 170.5/77.5

d ≤ 2.2

if they only take payment for whole days, he has 2 whole days

Answer:

a symbol usually a letter standing for an unknown numerical value in an equation

Step-by-step explanation:

Answer:

shouldn't it be 11 ft ???

Answer:

a) 39 meters

b) t = 1.8 seconds

Step-by-step explanation:

a)

To find the starting height of the riders, we just need to use the value of t = 0 in the equation of h(t):

h(0) = -9.8*0^2 - 5*0 + 39

h(0) = 39 meters

b)

To find when the height will be equal 0, we just need to use the value of h(t) = 0 and then find the value of t:

0 = -9.8*t^2 - 5*t + 39

Delta = b^2 - 4ac = 25 + 4*39*9.8 = 1553.8

sqrt(Delta) = 39.418

t1 = (5 + 39.418)/(-2*9.8) = -2.2662 s (A negative value for the time is not suitable for the problem)

t2 = (5 - 39.418)/(-2*9.8) = 1.756 s

Rounding to nearest tenth, we have t = 1.8 s

Answer:

(x - 10)² + (y + 4)² = 121

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (10, - 4 ) and r = 11 , then

(x - 10)² + (y - (- 4) )² = 11² , that is

(x - 10)² + (y + 4)² = 121

Answer: it would be 2.53

Step-by-step explanation: best answer

we know that we must add 29.8% more, in decimal form, to the net income in order to get the gross income.

Let's see the facts:

Income = $3,788

Withheld:

6.2% for social security

1.45% for medicare

16% for federal income tax

6.15% for state income tax

Now, with this given data, we can asseverate that the gross income is obtained by multiplying the net income by the sum of percentages as follows:

The sum of contributions: 6.2+1.45+16+6.15 = 29.8 %

So, we know that we must add 29.8% more,in decimal form, to the net income in order to get the gross income.

The gross income is:

Gross income= 3,788x 1.298

[Because 1 represents 100% and 0.298 represents %29.8]

Gross income = $4,916.82

The complete question is-

Cedric's monthly net income is $3,788. The following is withheld from him monthly gross income: 6.2% for social security • 1.45% for Medicare 16% for federal income tax 6.15% for state income tax Determine Cedric's monthly gross income. Round your answer to the nearest cent.

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Answer:

x < -80000.

Step-by-step explanation:

To solve the inequality 3600 + 1.02x < 2000 + 1.04x algebraically for x, you can start by subtracting 2000 + 1.04x from both sides of the inequality:

3600 + 1.02x - (2000 + 1.04x) < 2000 + 1.04x - (2000 + 1.04x)

1600 - 0.02x < 0

Then, you can divide both sides of the inequality by -0.02 to solve for x:

1600/-0.02 > 0/-0.02

-80,000 > x

The solution to the inequality is x < -80000.

You can check your solution by substituting -80000 into the original inequality:

3600 + 1.02(-80000) < 2000 + 1.04(-80000)

3600 - 81600 < 2000 - 832000

-45600 < -812000

Since -45600 is less than -812000, the solution x < -80000 is correct.

The random samples of 400 with true proportion in the range of the 27% to 32% correct option is ,

A. The result is not unusual as the probability which is p less than or equal to the sample proportion is 0.5, that is greater than 5%.

To determine whether it would be unusual for a random sample of 400 adults to result in 108 or fewer not owning a credit card,

Calculate the probability of obtaining such a result if the true proportion is within the expected range of 27% to 32%.

The sample proportion, denoted as p, can be calculated by dividing the number of adults who do not own a credit card by the total sample size.

Here, p = 108/400 = 0.27.

To determine the probability, use the normal approximation to the binomial distribution since the sample size is large (n = 400).

The mean of the binomial distribution is np, and the standard deviation is √(np(1-p)).

Here, np = 400 × 0.27

              = 108

and √(np(1-p)) = √(400 × 0.27 × 0.73)

                       ≈ 8.654.

To calculate the probability, standardize the value using the z-score formula,

z = (x - μ) / σ,

where x is the observed value, μ is the mean, and σ is the standard deviation.

For 108 or fewer adults not owning a credit card, the z-score is,

z = (108 - 108) / 8.654

  ≈ 0  

The probability that p is less than or equal to the sample proportion can be obtained by the z-score in the standard normal distribution calculator.

Since the z-score is 0, the corresponding probability is 0.5.

Therefore, for the given random samples the correct option is A. The result is not unusual because the probability that p is less than or equal to the sample proportion is 0.5, which is greater than 5%.

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Eight cattle spend the entire day inside the barn because they weren't among the herd that went outside to graze. So the correct option is C)

There were eight cattle present inside the barn the entire time. All but eight of the 23 cattle that Mr. González had in his stable left to go graze outside for six hours. We initially discover that 15 cattle were out grazing for six hours before calculating how many cattle were inside the barn all day.

We can presume that the eight cattle who didn't go outside to graze spent the entire day inside the barn because the problem provides no information on them. 8 cattle are so present within the barn all day.

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Answer:

c

Step-by-step explanation:

The general solution of the given differential equation: x(t) = c1×e^(-t) + c2×e^(5t) + t² - 4t + 4.

To find the general solution of the given differential equation, first solve the corresponding homogeneous equation: d²x/dt² - 2(dx/dt) - 5x = 0. The characteristic equation for this is: m² - 2m - 5 = 0. Solving this, we get m1 = -1 and m2 = 5. So, the general solution of the homogeneous equation is: x_h(t) = c1×e^(-t) + c2×e^(5t).

Next, we find a particular solution for the non-homogeneous equation. Let x_p(t) = At² + Bt + C. Differentiate twice to get the first and second derivatives, and plug them into the non-homogeneous equation to solve for A, B, and C. After doing this, we find that x_p(t) = t² - 4t + 4.

Finally, combine the homogeneous and particular solutions to get the general solution of the given differential equation: x(t) = c1×e^(-t) + c2×e^(5t) + t² - 4t + 4.

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Hey there!

In this picture, we have many pairs of adjacent angles:

1 and 2

2 and 4

4 and 3

3 and 1

This is because these pairs are being connected by a vertex and a side.

Hope it helps and have a great day!!!

The simplified expression is \(\frac{17}{6} x+\frac{2}{17} y\) - 3, obtained by distributing and combining like terms in the given expression. It represents the expression in a more concise and simplified form.

To simplify the expression 2(\(\frac{5}{3} x+\frac{2}{34}y -\frac{1}{4} x-1\frac{1}{2}\)), we can start by distributing the 2 to each term inside the parentheses.

The resulting expression would be:

(2 * 5/3x) + (2 * 2/34y) - (2 * 1/4x) - (2 * \(1\frac{1}{2}\))

Simplifying each term individually:

(10/3x) + (4/34y) - (2/4x) - (3)

Further simplifying:

(10/3x) + (2/17y) - (1/2x) - (3)

Combining like terms:

(10/3x - 1/2x) + (2/17y) - (3)

Finding a common denominator for the x-terms, we have:

[(20 - 3)/6x] + (2/17y) - (3)

Simplifying the x-terms:

(17/6x) + (2/17y) - (3)

This can be further rearranged to:

(17/6)x + (2/17)y - 3

Therefore, the simplified expression is (17/6)x + (2/17)y - 3.

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Answer:

(x + 1)(x + 2) is divisible by 3.

Step-by-step explanation:

Assume that x is not divisible by 3. This means that x can be expressed as x = 3k + r, where k is an integer and r is the remainder when x is divided by 3. Since x is not divisible by 3, the remainder r must be either 1 or 2.

Case 1: r = 1

If r = 1, then x = 3k + 1. Now let's consider (x + 1)(x + 2):

(x + 1)(x + 2) = (3k + 1 + 1)(3k + 1 + 2)

= (3k + 2)(3k + 3)

= 3(3k^2 + 5k + 2)

We can see that (x + 1)(x + 2) is divisible by 3.

Case 2: r = 2

If r = 2, then x = 3k + 2. Now let's consider (x + 1)(x + 2):

(x + 1)(x + 2) = (3k + 2 + 1)(3k + 2 + 2)

= (3k + 3)(3k + 4)

= 3(3k^2 + 7k + 4)

We can see that (x + 1)(x + 2) is divisible by 3.

Hence, the statement is proven.

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Answer: John walks a total of 360 yards from school.

Step-by-step explanation:

Let's represent the total distance John walks from school as "x".

According to the problem, John has already walked 15% of the way, which can be written as:

0.15x

We also know that he has walked 54 yards so far, which means:

0.15x = 54

To find the total distance John walks from school, we can solve for "x" by dividing both sides of the equation by 0.15:

x = 54 ÷ 0.15

x = 360

Therefore, John walks a total of 360 yards from school.

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Mary lou will have $20574.6 in her savings account when she is ready to enroll in college.

For given question,

Mary lou received $14,000, 7 years prior to her enrolling in college.

She invested the money at 5.5% compounded semiannually.

so the Principal(P) = $14000

Rate (R) = 5.5%

Period(t) = 7 years

First we find the rate of interest in decimal form.

5.5% = 5.5/100

5.5% = 0.055

so, r = 0.055

Using the formula for continuous compound interest,

\(\Rightarrow A = Pe^{rt}\\\\\Rightarrow A=14000\times e^{(0.055\times 7)}\)

⇒ A = 14000 × e^(0.385)

⇒ A = 14000 × 1.4696

⇒ A = $20574.6

This means, after 7 years she will have $20574.6 in her saving account.

Therefore, Mary lou will have $20574.6 in her savings account when she is ready to enroll in college.

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Answer:

20 cents more than the price of flower

Step-by-step explanation:

We can say that the probability of a household donating to both stations is likely lower than the probability of a household donating only to the public radio station, as donating to both stations would require a higher level of financial commitment.

To determine the probability of a household not donating to the public television station given that it donates to the public radio station, we would need to have data on the number of households that donate to both stations as well as the number of households that only donate to the public radio station. Without this information, it is not possible to calculate the probability.

However, we can say that the probability of a household donating to both stations is likely lower than the probability of a household donating only to the public radio station, as donating to both stations would require a higher level of financial commitment. To answer your question about the probability a household does not donate to the public television station given that they donate to the public radio station, we would need more information. Specifically, we would need the joint probability of donating to both stations and the probability of donating to the public radio station.

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Answer:

independent

Step-by-step explanation:

Answer:

125 Dollars

Step-by-step explanation:

Total fee = 7000

Amount in hand = 4000

Amount to be saved in 2 years = 7000 - 4000 = 3000

No of months in 2 years = 12 x 2 = 24

Per month saving = 3000 / 24 = 125 $

Answer:

vfssfdgddedt

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

You dilate a line segment around a point by following a simple procedure mentioned below that begins with identifying the center of a line segment.

Dilating a line segment around a point is a simple process. First, you need to identify the center of the line segment.

Then, use a ruler or other measuring device to measure the distance from the center of the line segment to each end point.

To dilate the line segment, multiply the measured distance by the desired scale factor. Finally, draw a new line segment connecting the two new end points.

This will give you the dilated line segment around the point you identified at the beginning.

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