10 POINTS AND BRAINLIEST!!

A government agency can spend at most $125,000 on a training program. If the training program has a fixed cost of $45,000 plus a cost of $125 per employee, how many employees can be trained?

Answer:

a testable proposition that explains an observed phenomenon or answers a question

Step-by-step explanation:

Basically an hypothesis is a theory given as a solution to a question proposed by a problem in from of you, but that it needs testing before it can be taken as truth or not

A hypothesis is an educated guess or a testable prediction drawn from observations. It is a tentative statement about reality that can be verified through experiments. If a hypothesis explains a large body of experimental data, it may evolve into a theory.

A hypothesis is a testable prediction about how the world will behave if our idea is correct. Observations and questioning may lead a scientist to form a hypothesis. In essence, a hypothesis is an educated guess or a tentative statement about reality that can be tested to determine its validity.

An example of a hypothesis is 'if I study all night, I will get a passing grade on the test'. The hypothesis, the educated guess in this scenario, then undergoes a process of testing through experimentation, calculation, and comparison with the experiments of others.

If a hypothesis is capable of explaining a large body of experimental data, it can reach the status of a theory. A theory in scientific terms is a well-substantiated, comprehensive, testable explanation of particular aspects of nature. However, theories can be modified if new data becomes available. This process of questioning, observing, hypothesizing, testing, and eventually forming a theory is known as the scientific method.

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Answer:

13665.6 deaths per year

Step-by-step explanation:

We can determine certain statistics based on the information. If 15567 patients where discharge and 245 deaths were recorded, the total number of patients were:

[tex]=15567+245=15812[/tex]

If 75 deaths occured in the first 48 hours we have a death rate of:

[tex]=75/48=1.56[/tex]

1.56 deaths per hour.

We want the death rate per year. If we have the death rate per hour we can determine the death rate per year:

[tex]1.56\cdot{24}\cdot{365}=13665.6[tex]

13665.6 deaths per year

The correct net death rate for the year is [tex]\(\frac{172}{15567}\).[/tex]

To calculate the net death rate for the year, we need to consider the total number of deaths that occurred and the total number of discharges. The net death rate is calculated by dividing the number of deaths by the number of discharges.

 From the given statistics, we have:

- Total discharges: 15,567

- Total deaths: 245

 However, we need to adjust the total deaths to account for the deaths that occurred under 48 hours and the medical examiner's cases, as these might not be included in the net death rate calculation.

- Deaths under 48 hours: 75

- Medical examiner's cases: 8

 The deaths under 48 hours and the medical examiner's cases are typically excluded from the net death rate calculation because they may not reflect the quality of care provided by the hospital. Therefore, we subtract these from the total deaths:

Adjusted deaths = Total deaths - Deaths under 48 hours - Medical examiner's cases

Adjusted deaths = 245 - 75 - 8

Adjusted deaths = 162

 Now, we can calculate the net death rate:

Net death rate =[tex]\(\frac{\text{Adjusted deaths}}{\text{Total discharges}}\)[/tex]

Net death rate = [tex]\(\frac{162}{15567}\)[/tex]

This gives us the net death rate for the year based on the adjusted number of deaths."

Answer:

One ml is equal to a cm3, then

m=2.67g/cm3*30.5cm3

m=81.435g

If we divide this quantity by 1000 to pass this to Kg we get:

m=81.435/1000=0.081435kg

Step-by-step explanation:

Remember the formula of density is density=mass/volume, if we solve for mass we get:

mass=density*volume

Answer:

x intercept- -2

12x - 8(0)= -24

12x = -24

x = -2

12(0)-8y = -24

-8y = -24

y = 3

y intercept

slope. 2/3

-8y = -12x - 24

y = (2/3)x + 3

Answer:

k=3

I mean the third choice

Step-by-step explanation:

f(x) = x-1

The required value of k is 3. Option C is correct.

Given that,
To find the value of k in the data set such that the data set represents a linear function.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
The slope of the function,
x, f(x) = (7,6) and (9,8)
Slope = 8 - 6 / 9 - 7
Slope = 2 / 2 = 1

Equation,
y + 3 = 1 (x + 2)
y = x - 1
Now at x = 4 : f(x) = k
k = 4 - 1
k = 3

Thus, the required value of k is 3. Option C is correct.

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Answer:

Option C 41%

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The number of people who own at most three t-shirts costing more than $19 each is equal to the number of people who own one t-shirt costing more than $19 each, plus the number of people who own two t-shirt costing more than $19 each, plus the number of people who own three t-shirt costing more than $19 each

Observing the graph

The number of people who own one t-shirt costing more than $19 each is 5

The number of people who own two t-shirt costing more than $19 each is 17

The number of people who own tree t-shirt costing more than $19 each is 23

The number of people who own at most three t-shirts costing more than $19 each is

[tex](5+17+23)=45\ people[/tex]

To find out the percentage divided the number of people who own at most three t-shirts costing more than $19 by one hundred eleven people (total people that shopped in a store) and then multiply by 100

[tex](45/111)100= 40.54\%[/tex]

Round to the nearest whole number

[tex]40.54\%=41\%[/tex]

The question involves the application of statistical principles to determine the percentage of people who own at most three expensive t-shirts. Assuming 59% is the correct answer, this means 66 out of the 111 people surveyed own three or fewer such t-shirts. The examples in the question references demonstrate the principles of economics, but aren't directly related to the question.

The question is about determining the percentage of people who own at most three t-shirts costing more than $19 each from a sample of 111 people. Given that the possible percentages provided are 21% and 59%, the process involves the application of statistical principles, particularly dealing with percentages in relation to a specific sample size. This example fits into a branch of mathematics known as statistics, which deals with data analysis, collection, interpretation, presentation, and organization.

Let's assume from the reference that 59% is the correct answer, this conveys that of the 111 people surveyed, approximately 66 people own three or fewer such t-shirts. This is obtained by calculating 59% of 111, which equals about 65.49 and rounds to 66.

In the references provided, there are examples of how the cost of t-shirts affects purchasing decisions. This is related to the principles of economics which involve opportunity cost and budget constraints, but is not directly tied to answering the initial question.

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Answer:

Answered below

Step-by-step explanation:

Sheet 1: Question 3

Vertically opposite angles are equal so you will equate the angles given,

∠LPN = ∠OPM

7 + 13x = -20 + 16x

27 = 3x

x = 9

Sheet 1: Question 4

Vertically opposite angles are equal so you will equate the angles given,

∠ABD = ∠EBC

2x + 20 = 3x + 15

-x = -5

x = 5

Sheet 1: Question 5

Step 1: Find the value of x

Vertically opposite angles are equal so you will equate the angles given,

∠SOP = ∠ROQ

5x = 4x + 10

x = 10

Step 2: Find angles

Angle SOP = 5x = 5(10) = 50°

Angle ROQ = 50° (because it is vertically opposite to angle SOP)

Angle SOR = 180 - 50 (because all angles on a straight line are equal to 180°)

Angle SOR = 130°

Angle POQ = 130° (because it is vertically opposite to angle SOR)

Sheet 1: Question 6

Angle 1 = 72° (because vertically opposite angles)

∠4 + ∠1 + 41 = 180° (because all angles on a straight line are equal to 180°)

∠4 + 72 + 41 = 180

∠4 = 67°

∠3 = 41° (because vertically opposite angles)

∠2 = 67° (because vertically opposite angles)

Sheet 2: Question 3

Step 1: Find the value of x

Sum of complementary angles is equal to 90°

Angle A + Angle B = 90°

7x + 4 + 4x + 9 = 90°

11x = 90 - 13

11x = 77

x = 7

Step 2: Find angle A and angle B using x

Angle A: 7x + 4

7(7) + 4

Angle A = 53°

Angle B: 4x + 9

4(7) + 9

Angle B = 37°

Sheet 3: Question 3

Step 1: Find the value of x

Sum of supplementary angles is equal to 180°.

Angle A + Angle B = 180°

3x - 7 + 2x + 2 = 180°

5x = 185

x = 37

Step 2: Find angle A and angle B using x

Angle A: 3x - 7

3(37)-7

Angle A = 104°

Angle B: 2x + 2

2(37) + 2

Angle B = 76°

Sheet 3: Question 4

Sum of supplementary angles is equal to 180°.

Step 1: Find x

1/4(36x-8) + 1/2(6x-20) = 180°

Take LCM

[36x - 8 + 2(6x - 20)]/4 = 180°

36x - 8 +12x - 40 = 180 x 4

48x - 48 = 720

48x = 768

x = 16

Step 2: Find both angles with the help of x

Angle 1: 1/4(36x-8)

1/4[36(16)-8] = 568/4

Angle 1 = 142°

Angle 2: 1/2(6x-20)

1/2[6(16)-20] = 76/2

Angle 2 = 38°

Sheet 4: Question 1

All angles on a straight line are equal to 180°

Angle z + 138° = 180°

Angle z = 180 - 138

Angle z = 42°

Sheet 4: Question 2

Linear pair 1: 5 and 7 (because both angles are on a straight line and are equal to 180°)

Linear pair 2: 6 and 8 (because both angles are on a straight line and are equal to 180°)

Sheet 4: Question 3

Step 1: Find the value of x

All angles on a straight line are equal to 180° or linear pairs are equal to 180°

Angle LMO + Angle OMN = 180°

7x + 20 + 10 + 5x = 180°

12x = 180 - 30

x = 150/12

x = 12.5

Step 2: Find angles using the value of x

Angle LMO: 7x + 20

7(12.5) + 20

Angle LMO = 107.5°

Angle OMN: 10 + 5x

10 + 5(12.5)

Angle OMN = 72.5°

Sheet 4: Question 4

Linear pairs are equal to 180°.

Angle 1 + Angle 2 = 180°

1/3(27x-6) + 1/2(6x-20) = 180°

Take LCM = 6

[2(27x-6) + 3(6x-20)]/6 = 180

54x - 12 + 18x - 60 = 1080

72x - 72 = 1080

72x = 1152

x = 16

!!

The average distance of Mercury from the Sun is found using the formula E(x) = 0.2x^3/2, where E(x) = 88 days, which is the year length for Mercury. Solving for x, the distance comes out to be approximately 57.9 million kilometers.

The question asks us to determine the average distance of Mercury from the center star, which can also be understood as the Sun, given that its year (the period it takes to orbit the Sun) is approximately 88 Earth days. We are provided with the formula E(x) = 0.2x3/2, where E(x) represents the number of Earth days in a planet's year and x is the planet's average distance from the Sun in millions of kilometers.

To solve for x, we set E(x) equal to 88 days and solve for x.

E(x) = 88
0.2x3/2 = 88
x3/2 = 88 / 0.2
x3/2 = 440
Now we take both sides to the power of 2/3 to solve for x.
x = 4402/3

To find the value of x, we calculate 440 raised to the 2/3 power.

x = 4402/3
≈ 57.9

Therefore, the average distance of Mercury from the Sun is approximately 57.9 million kilometers.

The answer is 240000

Step-by-step explanation:

When you round 620 to the nearest hundred,you will get 600

and when you round 374 to the nearest hundred,you will get 400

multiplying the product after rounding them will give 600×400

=240000

The estimated product when 620 and 374 are rounded to the nearest hundred and multiplied is 240000.

Product is the output obtained when two numbers are multiplied.

The product has to be obtained of numbers 620 and 374

Rounding to nearest hundred

620 can be written as 600

374 can be written as 400

=> 600 * 400

= 240000

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Answer:

Step-by-step explanation:

Given that an advertiser wishes to estimate the proportion of adults in Utah who already own a gym membership.

Confidence level wanted = 90%

Critical value Z for 90% = 1.645

p is not known hence for maximum std error we know p =0.5

Let us take p =0.5

Margin of error = [tex]1.645*\sqrt{\frac{pq}{n} } =\\1.645*0.5(\frac{1}{\sqrt{n} } ) 0.10\\n=67.65\\n~68[/tex]

Sample size can be 68

Answer: now, the expected value will be x = p1*0$ + p2*1$

where p1 is te probabilty of a fail and p2 the probability of succes.

Ok, we will have 4 steps here.

1) there are 4 balls, and if we chose a spesific colour, there are 50% chance of succes. x = 0.5$

2) there are 3 balls, but yo know that if in the first step you graved a blue ball, then here you have a 66% of getting a red one, so if you play optimaly, you will guess red. x = 0.6$

3a) now there are two posibilities, in the last step yo get the other blue ball, so now are two red balls in the box, and you have guaranted 2 bucks. x = 2$ (but you failed in the last step)

3b) if in 2 you get a red ball, then again you have a 50/50 chance for each colour. x= 0.5$

4) there's only one ball in the box, you get a dollar x = 1 $

so if you go with the 3b path, te expected value will be 2.6$

with 3a) x = 2.5$

The expected value of playing this game, if you play optimally, is $0.83.

To calculate the expected value of this game, we need to determine the probability of each outcome and multiply it by the corresponding payout. Let's start with the first draw:

For the second draw, there are two possibilities:

To calculate the expected value, we multiply each outcome by its probability and sum them up:

(2/4) * $1 + (2/4) * $1 + (1/3) * $1 + (1/3) * $1 = $0.83

The expected value of this game, if you play optimally, is $0.83.

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Answer:

12x²√2z

Step-by-step explanation:

Given to simplify

3√32x⁴z

This can be written as

3* √32 *√x⁴ *√z--------------------------break down into terms

3*√16*√2*√x⁴*√z------------------------identifying perfect squares

3 * 4* √2 * x² *√z---------------------------collect like terms

12 * x² * √2 * √z-----------------------multiplication

12x² *√2z------------------------puting terms under same root together

12x²√2z

Answer:

Step-by-step explanation:

note : an equation is : y - b = m(x - a)    ... the point is : A ( a , b) and slope : m

in this exercice :  m= - 8     and  a= - 3    and b= -6

an equation is : y+6 = -8(x+3)

you can write :   y+6 = - 8x -24

8x+y = - 30 .....answer : C

Answer:

C. 8x + y = -30

Step-by-step explanation:

-6 = -8[-3] + b

24

-30 = b

y = -8x - 30

+8x +8x

___________

8x + y = -30 >> Standard Linear Equation

* This is the fastest way to do it.

I am joyous to assist you anytime.

Answer:

Option A - 342 feet

Step-by-step explanation:

Given : Janice puts a fence around her rectangular garden. The garden has a length that is 9 feet less than 3 times its width.

To find : What is the perimeter of Janice fence if the area of her garden is 5,670 square feet?

Solution :

Let the width of the garden be w=x feet.

The garden has a length that is 9 feet less than 3 times its width.

The length of the garden be l=3x-9 feet

The area of the garden is A=5670 square feet.

The formula of area of garden is [tex]A=l\times w[/tex]

[tex]5670=(3x-9)\times x[/tex]

[tex]5670=3x^2-9x[/tex]

[tex]3x^2-9x-5670=0[/tex]

[tex]x^2-3x-1890=0[/tex]

[tex]x^2-45x+42x-1890=0[/tex]

[tex]x(x-45)+42(x-45)=0[/tex]

[tex](x-45)(x+42)=0[/tex]

[tex]x=45,-42[/tex]

Reject x=-42 as measurement cannot be negative.

The width of the garden is w=45 feet.

The length of the garden is l=3(45)-9=135-9=126 feet.

The perimeter of the garden is [tex]P=2(l+w)[/tex]

[tex]P=2(126+45)[/tex]

[tex]P=2(171)[/tex]

[tex]P=342[/tex]

The perimeter of Janice fence is 342 feet.

Therefore, Option A is correct.

The perimeter of Janice's fence is: [tex]\[ {342 \text{ feet}} \][/tex]

To determine the perimeter of Janice's garden, let's follow these steps:

Step 1: Define Variables

Let ( w ) be the width of the garden in feet.

The length ( l ) of the garden is given by: [tex]\[ l = 3w - 9 \][/tex]

Step 2: Set Up the Area Equation

The area of the rectangular garden is given as 5,670 square feet:

[tex]\[ \text{Area} = l \times w \][/tex]

[tex]\[ 5670 = (3w - 9) \times w \][/tex]

Step 3: Solve the Quadratic Equation

Expand and simplify the equation:

[tex]\[ 5670 = 3w^2 - 9w \][/tex]

Rearrange it to standard quadratic form:

[tex]\[ 3w^2 - 9w - 5670 = 0 \][/tex]

Step 4: Factor or Use the Quadratic Formula

Divide through by 3 to simplify:

[tex]\[ w^2 - 3w - 1890 = 0 \][/tex]

Solve using the quadratic formula [tex]\( w = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)[/tex]:

[tex]\[ a = 1, \, b = -3, \, c = -1890 \][/tex]

[tex]\[ w = \frac{-(-3) \pm \sqrt{(-3)^2 - 4 \cdot 1 \cdot (-1890)}}{2 \cdot 1} \][/tex]

[tex]\[ w = \frac{3 \pm \sqrt{9 + 7560}}{2} \][/tex]

[tex]\[ w = \frac{3 \pm \sqrt{7569}}{2} \][/tex]

[tex]\[ w = \frac{3 \pm 87}{2} \][/tex]

This gives two potential solutions:

[tex]\[ w = \frac{90}{2} = 45 \][/tex]

[tex]\[ w = \frac{-84}{2} = -42 \][/tex]

Since width cannot be negative:

[tex]\[ w = 45 \][/tex]

Step 5: Find the Length

Substitute ( w = 45 ) into the length equation:

[tex]\[ l = 3(45) - 9 \][/tex]

[tex]\[ l = 135 - 9 \][/tex]

[tex]\[ l = 126 \][/tex]

Step 6: Calculate the Perimeter

[tex]\[ P = 2l + 2w \][/tex]

[tex]\[ P = 2(126) + 2(45) \][/tex]

[tex]\[ P = 252 + 90 \][/tex]

[tex]\[ P = 342 \][/tex]

Thus, the perimeter of Janice's fence is: [tex]\[ {342 \text{ feet}} \][/tex]

Answer:

C. A distinguishing mark of a profession is its acceptance of responsibility to the public.

Step-by-step explanation:

The following statement best explains why the auditing profession has found it essential to promulgate ethical standards and to establish means for ensuring their observance is :

A distinguishing mark of a profession is its acceptance of responsibility to the public.

The best explanation for why ethical standards are crucial in auditing is that professions are expected to be responsible to the public, ensuring trust, honesty, and integrity in their actions which align with their ethical codes.

The statement that best explains why the auditing profession has found it essential to promulgate ethical standards and to establish means for ensuring their observance is: C. A distinguishing mark of a profession is its acceptance of responsibility to the public. This underscores the basic principle that professionals, such as auditors, have a duty to act in the public interest and maintain public confidence in the profession. Professionals act as gatekeepers in various industries, ensuring that a company's actions uphold the law and adhere to established standards, thus serving the public good by promoting honesty and integrity.

Moreover, professions such as law, medicine, and accounting require professional education and licensing to ensure legal and ethical behavior, with mandated Codes of Ethics that outline the accountability to those served and to the profession itself. Therefore, the maintenance of ethical standards and the enforcement thereof are essential to professional integrity and the protection of public interests.

Answer: 4,85 meters

Step-by-step explanation:

Using energy we get the velocity when the man gets to the bottom of the hill

mgh=1/2 m v^2

Then the velocity is the squareroot of two times the mass times the gravity constant =9,598 m/s2

Using energy again, we can get the velocity on the edge of the ledge (using the second mass, the one of the man plus the backpack)

1/2 M1 V1^2=1/2 M2 V2^2

We get V2=8,24 m/s2

Then we have to analyze the jump, horizontally, with constant velocity, and vertically, with constant acceleration equals to the gravity constant.

To get the time we analyze the vertical move

Y=1/2 g t^2

t=59 seconds

To get the horizontal distance we use

X= v t

X=4,85 meters.

Answer:

The answer to your question is: 35 questions worth 2 points and 15 questions worth 3 points.

Step-by-step explanation:

Data

Number of questions = 50

Total points = 115

x = questions worth 2 points

y = questions worth 3 points

Process

write to equations

(1)  ---------------    x + y = 50

(2) --------------    2x + 3y = 115

Solve them by substitution

           x = 50 - y

         2 (50 - y) + 3y = 115

          100 - 2y + 3y = 115

           3y -2 y = 115 - 100

                     y = 15

           x = 50 - 15

            x = 35

Answer:

 the quantities do NOT vary directly

Step-by-step explanation:

A graph showing a proportional relationship is a straight line through the origin. This graph goes through (0, 100), so does NOT show a proportional relationship. y does NOT vary directly with x.

The correct answer is:

Option C: 5(2x^5+x^2−3)

A Quick Check:

5*2x^5 is 10x^5

5*x^2 is 5x^2

and 5*-3 is -15

making the equations match

The factored form of the expression 10x⁵ + 5x² - 15 is 5(x⁵ + x² - 3).

A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.

Given, A polynomial of degree five which is 10x⁵ + 5x² - 15.

Now, The HCF of 10, 15, and 5 is 5, and the HCF of x⁵, x², and x⁰ is x⁰ = 1.

Therefore,

10x⁵ + 5x² - 15.

= 5x⁰(x⁵ + x² - 3).

= 5(x⁵ + x² - 3).

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Answer:

The Andrew equitation is 4 times more bigger than Peter equation.

Step-by-step explanation:

(16x-8x=40) is:

4*(4x-2=10)=(16x-8=40)

Final answer:

Approximately 0.3% of IQ scores are greater than 133 according to the empirical rule, which states that 99.7% of values fall within three standard deviations of the mean in a bell-shaped distribution.

Explanation:

Using the empirical rule (also known as the 68-95-99.7 rule) for a bell-shaped distribution, we can determine the percentage of IQ scores that fall at different distances from the mean.

A score of 133 is three standard deviations above the mean (since the mean is 97 and the standard deviation is 12, 97 + 3(12) = 133). According to the empirical rule, approximately 99.7% of IQ scores fall within three standard deviations of the mean. Therefore, to find the percentage of scores greater than 133, we subtract the bottom 99.7% from 100%, resulting in approximately 0.3%.

Thus, following the empirical rule, 0.3% of IQ scores are greater than 133.

Answer:

21

Step-by-step explanation:

You were close to de answer but you rounded in a wrong way

If we calculate [tex]\sqrt{16^{2} + 14^{2}}[/tex]  we get 21.2602916255

We need to round to the nearest whole number, it means that we have we only have two options: 21 or 22

We need to remember the rounding rules:

We see that 1 is followed by 2, it means that we have to round the number down, so our answer is 21

Answer:

  D' = (4, -1)

Step-by-step explanation:

Translation down by 2 units subtracts 2 from the y-coordinate. The x-coordinate remains unchanged. You can see this in the descriptions of C and C':

Likewise:

__

The translated segment is still a horizontal segment, now at y=-1 instead of at its previous position of y=1.

Answer:

I guess u want to know the quadratic function and its formula is, AX*2 + BX + C. Otherwhise you want to know how to get 0 and get the Xm if you want to know how to solve a quadratic. That formula is,  (-B +/- [tex]\sqrt{x}[/tex] (B*2 - 4AC) ) . 1/2 (where A, B and C are the number at the original function).

Step-by-step explanation:

I think it 8 I think this is the right answer

Answer:

g(3) = 34

Step-by-step explanation:

To evaluate g(3) substitute x = 3 into g(x), that is

g(3) = 4(3)² - 3(3) + 7 = (4 × 9) - 9 + 7 = 36 - 9 + 7 = 34

Answer:

Let the number of hours traveled by train be "x".

The x = the number of hours traveled by plane.

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

Equation:

train distance + plane distance = 1300 miles

50x + 275x = 1300

x(325) = 1300

x = 4 hours

---

The trip took 8 hrs.

Step-by-step explanation:

Trust me

Answer:

The answer to your question is: time = 4 hours

Step-by-step explanation:

Data

Total distance = 1300 miles

train v = 50 mi/h      time is the same        distance = x

plane v = 275 mi/h                                      distance = 1300 - x

t = ?

Formula

v = d/t

Process

Train  t = d/v           t = x / 50

Plane  t = d/ v         t = (1300 - x) / 275

                   x / 50   =  (1300 - x) / 275

                  275 x  = 50 (1300 - x)

                  275 x = 65000 - 50x                   solve for x

                  275x + 50x = 65000

                  325x = 65000

                  x = 65000/325

                  x = 200

   Time with train

                                t = 200 / 50 = 4 hours

Time with plane

                               t = (1300 - 200) / 275

                               t = 1100 / 275 = 4 hours

Answer:

the 3 yard line

Step-by-step explanation:

Answer:

B. $25,069

Step-by-step explanation:

An interest of 6% per year, compounded monthly it means that he earns 6/12% = 0.5% of what he has invested every month.

If he invests x money what he will have the first month will be :

Money = x*(1+0.005)

The next month:

Money' = Money*(1+0.005) = x *(1+0.005)(1+0.005) = x* (1+0.005)^2

Therefore in this type of interest the formula is:

Money = x*(1+r)^n

Where:

x is the money invested the first time

r is the interest

n is the number of periods

For this problem:

x = what you have to find

r = 0.005

n = 3 years (1 period is 1 month) then the period is 36 months

Money = 30000

Replacing:

30000 = x * (1+0.005)^36

x = 25,069

Final answer:

To make a $30,000 down payment in three years with an account earning 6% interest compounded monthly, James needs to deposit approximately $25,189.06 today.

Explanation:

Calculating the Present Value for a Future Goal

To achieve a $30,000 down payment in three years with an account that earns 6% interest per year, compounded monthly, we need to calculate the present value of the future goal. Since the interest is compounded monthly, we use the present value formula for compound interest, which is P = A / (1 + r/n)^(nt), where P is the present value, A is the future amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

Here, A = $30,000, r = 0.06 (6% converted to decimal), n = 12 (compounded monthly), and t = 3.
So, P = $30,000 / (1 + 0.06/12)^(12*3) = $30,000 / (1 + 0.005)^(36) ≈ $30,000 / 1.191016 = $25,189.06 (rounded to 2 decimal places).

The amount James needs to deposit today is approximately $25,189.06.

Answer:

b. 20%

Step-by-step explanation:

The distribution of  number of hours worked by students is:

0 - 10          =         20

10 - 20        =         80

20 - 30       =         200

30 - 40       =         100

Total number of students = 400

We need to find the percentage of students working between 10 and 20 hours. From the above table we can see that number of students working between 10 and 20 hours is 80. Now we need to convert this into percentage. What we need to evaluate is what percentage of 400 is 80.

The formula for percentage is:

[tex]\frac{\text{Concerned Value}}{\text{Total Value}} \times 100\%[/tex]

Concerned value is 80, total value is 400. So using these in the formula we get:

[tex]\frac{80}{400} \times 100%\\\\  = 20\%[/tex]

Thus, 20% of the students are working between 10 and 20 hours.

The percentage of statistics students working between 10 and 20 hours per week is 20%, which is calculated by dividing the frequency of the group (80 students) by the total number of students (400) and multiplying by 100.

The question is asking us to find the percentage of statistics students who work between 10 and 20 hours per week, given the frequency distribution provided in Exhibit 2-1. According to the exhibit, 80 students work between 10 and 20 hours per week. Since the total number of students is 400, we calculate this percentage by taking the number of students in the given category (80 students) and dividing it by the total number of students (400), then multiplying by 100 to get a percentage.

The calculation is:

Percentage = (80 ÷ 400) × 100

Percentage = 0.20 × 100

Percentage = 20%

Therefore, the percentage of students working between 10 and 20 hours is 20%, which corresponds to option b.