Vicky has 2 jobs offers for teaching. She just finished her Master’s Degree in mathematics education.

A. She can work at Southside High School as a teacher with a base salary of $43,600 per year. She will also coach JV softball which will add another $900 to her annual salary. The contract suggests the school will be expecting her 190 days but she will be provided with 10 sick days. So, she must actually work a minimum of 180 days (any less and her salary will be reduced). Each day will consist of 8 working hours. With this school she will be provided with free life insurance for $15,000 of coverage. Her health & dental or medical premiums are $78/month. Finally, the school system would require her to automatically invest 5% of his her monthly income for retirement.

B. She can work at Central Tech College as a math instructor. She will be paid $900 for each credit hour she teaches. During the course of her first year of teaching, she would teach a total of 50 credit hours. The college expects she will work a minimum of 170 days (any less and the salary would be reduced) and 8 hours each day. At the college she will have to pay $3 per month for a life insurance policy of $25,000. Her health & dental or medical premiums are $85 per month. Finally, the company would require her to automatically invest $200 per month for retirement.

What is Vicky's Gross Monthly Income for the job at Southside High School?

Answer:

There is no such point where the given curve has a tangent line with slope 2.

Step-by-step explanation:

We have been given a curve [tex]y=4x^3+7x-5[/tex]. We are asked to show that the given curve has no tangent line with slope 2.

First of all, we will find the derivative of given curve as shown below:

[tex]y'=\frac{d}{dx}(4x^3)+\frac{d}{dx}(7x)-\frac{d}{dx}(5)[/tex]

[tex]y'=4\cdot 3x^{3-1}+7x^{1-1}-0[/tex]

[tex]y'=12x^{2}+7x^{0}[/tex]

[tex]y'=12x^{2}+7(1)[/tex]

[tex]y'=12x^{2}+7[/tex]

We know that derivative represents slope of tangent line, so we will equate derivative of the given curve with 2 and solve for the point (x), where the slope of tangent line will be equal to 2 as:

[tex]12x^2+7=2[/tex]

[tex]12x^2+7-7=2-7[/tex]

[tex]12x^2=-5[/tex]

[tex]x^2=-\frac{5}{12}[/tex]

We know that square of any real number could never be negative, therefore, there is no such point where the given curve has a tangent line with slope 2.

Final answer:

The proof involves finding the derivative of the given curve y = 4x³ + 7x - 5, setting it equal to the desired slope (2), and showing that the resulting equation has no real solutions, proving that no tangent line with slope 2 exists for this curve.

Explanation:

The question is about proving that the curve y = 4x³ + 7x - 5 does not have any tangent line with slope 2. To do this, we first need to find the derivative of the curve, which gives us the slope of the tangent at any point (x). The derivative of y with respect to x is given by y' = 12x² + 7. To determine if a tangent with slope 2 exists, we set the derivative equal to 2 and solve for x: 12x² + 7 = 2.

Solving this equation gives us 12x² = -5, which has no real solution since the left side of the equation (a squared term) cannot be negative. This means there is no value of x for which the slope of the tangent (derivative) is equal to 2, proving that no such tangent line exists for the given curve.

Answer:

2.25 miles.

Step-by-step explanation:

Given,

In map, the scale is, 1 inch = 3 miles,

That is, the number of miles in 1 inch = 3,

The number of miles in 0.75 inch = 0.75 × number of miles in 1 inch,

                                                       = 0.75 × 3

                                                       = 2.25

Thus, 0.75 inch = 2.25 miles.

According to the question,

Distance from home to school in scale = 0.75 inch

Hence, the actual distance from home to school is 2.25 miles.

Answer:

2.25

Step-by-step explanation:

Answer:

(a)Area of the bedroom=96 square inches

(b)Area of the living room =144 square inches

(c)Area of the dollhouse that is not of the bedroom or living room =336 square inches.

Step-by-step explanation:

The area of the bedroom is 1/6 the area of the entire dollhouse

The area of the living room is 3/2 times the area of the bedroom.

The area of the entire dollhouse is 576 square inches

Let the area of bedroom=b

Let the area of living room=l

(a) The area of the bedroom is 1/6 the area of the entire dollhouse

[tex]b=\frac{1}{6}X576=96[/tex] square inches

(b)The area, in square inches, of the living room

The area of the living room is 3/2 times the area of the bedroom

l= [tex]\frac{3}{2}X96=144[/tex] square inches

(c)The total area of the house =576 square inches

Area of the bedroom=96 square inches

Area of the living room =144 square inches

Area of the dollhouse that is not of the bedroom or living room

=576-(96+144)=576-240=336 square inches.

The area of the living room is 3/2 times the area of the bedroom

This is gotten by subtracting the area of the bedroom and living room from the total area of the house.

Answer:

d) (179.20, 212.716)

Step-by-step explanation:

1000 : 345

569 : 195.96

Midpoint of (179.20, 212.716) is 195.958 which is the closest to 195.96

Final answer:

The interval estimate for passengers expected to carry more than one piece of luggage on a full Boeing 747 is (179.20, 212.716), calculated using the sample proportion and the standard error for a 95% confidence interval.

Explanation:

To determine an interval estimate of the number of passengers that would be expected to carry more than one piece of luggage on a domestic Boeing 747 with a capacity of 568 passengers, we use the sample proportion of passengers with more than one bag from the given sample, which is 345 out of 1000 passengers. This sample proportion, denoted as p-hat, is 0.345. We will use this proportion to estimate the population proportion in the domestic Boeing 747, assuming the plane is at full capacity.

We can calculate the estimated number of passengers by multiplying the proportion (p-hat) by the capacity of the plane. For a Boeing 747 with 568 passengers, this would be 0.345 * 568. To build an interval estimate, we also need to calculate the standard error (SE) of the proportion which is given by the formula SE = sqrt(p-hat*(1-p-hat)/n), where 'n' is the sample size. With a sample size of 1000, the SE can be calculated and then used to construct the 95% confidence interval using the Z-score for 95% confidence (approximately 1.96).

After calculating the interval estimate, we find that the confidence interval falls within one of the options provided. The correct interval estimate of the number of passengers expected to carry more than one piece of luggage on the plane, assuming it's full, would be (179.20, 212.716), which corresponds to option d.

Answer: 0.206

Step-by-step explanation: the probability of employees that needs corrective shoes are =8%= 8/100 = 0.08

Probability of employees that needs major dental work = 15% = 15/100 = 0.15

Probability of employees that needs both corrective shoes and dental work = 3% = 3/100 = 0.03

The probability that an employee will need either corrective shoes or major dental work = (Probability an employee will need correct shoes and not need dental work) or (probability that an employee will need dental work or not corrective shoes)

Probability of employee not needing corrective shoes = 1 - 0.08 = 0.92

Probability of employee not needing dental work = 1 - 0.15 = 0.85

The probability that an employee will need either corrective shoes or major dental work = (0.08×0.85) + (0.15×0.92) = 0.068 + 0.138 = 0.206 = 20.6%

The probability that an employee will need either corrective shoes or dental work = 0.206.

Please note that the word "either" implies that we must choose one of the two options (corrective shoes or dental work) and not both.

The  probability that an employee selected at random will need either corrective shoes or major dental work is 0.206.

Since

The exams showed that 8% of the employees needed corrective shoes, 15% needed major dental work, and 3% needed both corrective shoes and major dental work.

So,

Probability of employee not needing corrective shoes should be

= 1 - 0.08

= 0.92

And,

Probability of employee not needing dental work should be

= 1 - 0.15

= 0.85

So final probability should be

= (0.08×0.85) + (0.15×0.92)

= 0.068 + 0.138 = 0.206

= 20.6%

hence, The  probability that an employee selected at random will need either corrective shoes or major dental work is 0.206.

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Final answer:

To calculate John Worker's tax, we need to use the tax rate schedule. Assuming the taxable income is $31,000, we can refer to the tax rate schedule to determine the tax. If the tax rate for the income range $30,001 to $40,000 is 20%, then John Worker's tax would be 20% of his taxable income of $31,000, which equals $6,200.

Explanation:

To calculate John Worker's tax, we need to use the tax rate schedule. Assuming the taxable income is $31,000, we can refer to the tax rate schedule to determine the tax.

From the given information, we don't have the specific tax rate for $31,000. However, we can use the tax rates provided in the table to calculate the tax.

For example, if the tax rate for the income range $30,001 to $40,000 is 20%, then John Worker's tax would be 20% of his taxable income of $31,000, which equals $6,200.

Answer: he invested $5300 at 11% and $1000 at 6%

Step-by-step explanation:

Let x represent the amount which he invested in the first account paying 11% interest.

Let y represent the amount which he invested in the second account paying 6% interest.

He Invest $6,300 in two different accounts the first account paid 11% the second account paid 6% in interest. This means that

x + y = 6300

The formula for determining simple interest is expressed as

I = PRT/100

Considering the first account paying 11% interest,

P = $x

T = 1 year

R = 11℅

I = (x × 11 × 1)/100 = 0.11x

Considering the second account paying 6% interest,

P = $y

T = 1 year

R = 6℅

I = (y × 6 × 1)/100 = 0.06y

At the end of the year, he had earned $643 in interest , it means that

0.11x + 0.06y = 643 - - - - - - - - - -1

Substituting x = 6300 - y into equation 1, it becomes

0.11(6300 - y) + 0.06y = 643

693 - 0.11y + 0.06y = 643

- 0.11y + 0.06y = 643 - 693

- 0.05y = - 50

y = - 50/ - 0.05

y = 1000

x = 6300 - y = 6300 - 1000

x = 5300

Answer:

D. 28

Step-by-step explanation:

If a distribution is negatively skewed, the mean of the distribution is always less than the median.

If the median of a negatively skewed distribution is 31, then from the given options, the only value that is less than 31 is 28.

Therefore the mean could be 28.

The correct answer is D

Answer:

0

Step-by-step explanation:

In my opinion, the string won't display because, the intCount was not initialized before you started outputting the "Hi" string. So in order fro you to get the string to appear, the control point or value has to be initialized to maybe 0. then you can start looping from there. And if you are looping from the top or using greater than (>), The loop works best buy subtracting the control value else, you can end up with infinity loop.

Answer:

Step-by-step explanation:

Given that Alice and Bob race two toy trains around a circular track. The trains move in the same direction and they meet every 120 seconds. If Alice's and Bob's toy trains move in opposite directions, at constant rates, they meet every 30 seconds

Circular track is 1800 m.

Let speed be x and y respectively

When in same direction relative speed = x-y and when in opposite directions =x+y

30(x+y) = 1800

x+y= 60

120(x-y) = 1800

x-y = 15

Solving x = 37.5 m/hr and y = 12.5 per hour.

When Alice and Bob's toy trains move in the same direction, their relative speed is the sum of their individual speeds. When they move in opposite directions, their relative speed is the difference between their individual speeds. By solving simultaneous equations, we find that Alice's toy train has a speed of 75 m/s and Bob's toy train has a speed of 60 m/s.

Let's assume the speed of Alice's toy train is x m/s and the speed of Bob's toy train is y m/s.

When the trains move in the same direction, they meet every 120 seconds. Since they meet once every 30 seconds when moving in opposite directions, their relative speed is the sum of their individual speeds. So, when they move in the same direction, their relative speed will be x + y and when they move in opposite directions, their relative speed will be x - y.

When they move in the same direction, the distance covered by Alice's toy train in 120 seconds will be equal to the distance covered by Bob's toy train in 120 seconds, which is equal to the length of the circular track (1800 m). So, the equation can be written as:

Simplifying the equation, we get:

Similarly, when they move in opposite directions, the distance covered by Alice's toy train in 30 seconds will be equal to the distance covered by Bob's toy train in 30 seconds:

Simplifying the equation, we get:

Solving the equations simultaneously, we find that x = 75 m/s and y = -60 m/s. Since speed is always positive, we consider the magnitude of the velocity. Therefore, the speed of Alice's toy train is 75 m/s and the speed of Bob's toy train is 60 m/s.

Answer:

Hi, the correct answer to this would be  B, INCONSISTENT.

I researched this and my cite is www.quizlet.com. It is this answer because it is not consistent Nor C,D.

Step-by-step explanation:

I answered this before but someone deleted every single question I ever answered. Hahaha

Hope this helps :)

Answer:

The answer is CONSISTENT AND DEPENDENT

Step-by-step explanation:

USA Test Prep

Option B:

f(3) = 5

Solution:

Given function:

[tex]f(x)=\left\{\begin{aligned}-x^{2}, \ \ & x<-2 \\3, \ \ &-2 \leq x<0 \\x+2, \ \ & x \geq 0\end{aligned}\right.[/tex]

To find the value of f(3):

Here x value is 3 which is greater than 0 (3 > 0).

Therefore, f(x) = x + 2.

Substitute x = 3 in the above function.

f(3) = 3 + 2

f(3) = 5

Hence option B is the correct answer.

Answer:

it depends on if i think i could succeed in tha job

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

Mean is not a good measure of the centre because 150,000 is an outlier

Mode is $33,000

Median is $39,500

[(33000+46000)/2 = 39500]

Answer:

5in x 10in

Step-by-step explanation:

Solution:

1.  You have to assume that the ring will land on the board and as a result, just focus on one rectangle of the board since they are all the same size.  

2.  For the ring to land entirely inside the rectangle, the center of the ring needs to be 1.5 inches inside the border (radius is 1.5 inches), so the "winning rectangle" will have dimensions:

                               L = (x - 2(1.5)) = x - 3

                              w = (2x - 2(1.5)) = 2x-3.

3.  Now, we will set up and solve our geometric probability equation.  The winning rectangle's area of (x-3)*(2x-3) divided by the total rectangle's area of x*(2x) = 28%

                                (2x-3)*(x-3)/(2x^2) = .28

                                2x^2 - 9x + 9 = .56x^2

                                1.44x^2 - 9x + 9 = 0

4 .  Now you can plug that in the quadratic formula and get the solutions x = 1.25 or 5.  However, it cannot by 1.25 because that is too small of a dimension for the the circle with diameter of 3 to fit in, the answers has to be 5.

5. As a result, the dimensions of the rectangles are 5in x 10in.  

The game Ring Ding involves throwing a wooden ring onto a rectangular grid; the exact dimensions of the rectangles cannot be determined only with the provided information including the 28% win probability.

This is a question of probability concerning how a carnival game has been designed. Specifically, the game Ring Ding involves throwing a wooden ring onto a grid of rectangles without the ring touching any lines. Unfortunately, the question doesn't provide sufficient information to determine the exact dimensions of each rectangle. While it mentions the diameter of the ring and the relative dimensions of the rectangles (being twice as long as they are wide), the 28% chance of winning does not give a direct way to calculate the rectangle's dimensions as it depends upon other factors as well like player's skill, distance, angle of throw, etc.

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The length of MK is 9

Explanation:

The length of the sides are [tex]J K=36[/tex] , [tex]\mathrm{JL}=48[/tex] , [tex]J N=60[/tex]

We need to determine the length of MK

From the figure, we can see that JMN is a triangle and KL is parallel to MN.

Then, by side - splitter theorem, we have,

[tex]\frac{JK}{KM} =\frac{JL}{LN}[/tex]

where [tex]J K=36[/tex] , [tex]\mathrm{JL}=48[/tex]

The length of LN can be determined by subtracting JN and JL.

Thus, we have,

[tex]LN=JN-JL[/tex]

[tex]LN=60-48=12[/tex]

The length of LN is [tex]LN=12[/tex]

Substituting the values [tex]J K=36[/tex] , [tex]\mathrm{JL}=48[/tex] and [tex]LN=12[/tex] in [tex]\frac{JK}{KM} =\frac{JL}{LN}[/tex], we have,

[tex]\frac{36}{KM} =\frac{48}{12}[/tex]

Multiplying both sides by 12, we have,

[tex]\frac{36\times 12}{KM} =48[/tex]

 [tex]\frac{432}{KM} =48[/tex]

  [tex]\frac{432}{48} =KM[/tex]

     [tex]9=KM[/tex]

Thus, the length of MK is 9

Answer:

The correct option is

d) (179.20, 212.716)

Step-by-step explanation:

We have out of a random sample of 1000, 345 carried more than a bag

Therefore in the question our X = 345 passengers carry more than a piece of luggage

n = 1000

Therefore the probability of a passenger carrying more than one luggage = 345/1000 = 0.345

The confidence interval estimator of p is given by

[tex]p'+/-z_{\alpha/2}\sqrt{\frac{p'(1-p')}{n} }[/tex] where p' = 0.345 = probability of desired outcome

n = 1000 = Population size

z at 95 %   = Confidence interval estimate, the value is sought from the distribution table as z value is 1.96 at 95 % confidence level

We have  [tex]0.345+/-1.96\sqrt{\frac{0.345*(0.655)}{1000} }[/tex] which gives

0.3745 or 0.3155

Which gives the range of confidential interval estimate as

212.695 to 179.224 which is equivalent to

d) (179.20, 212.716).

To determine the interval estimate of the number of passengers carrying more than one piece of luggage on the plane, we use the formula for the confidence interval for a proportion. The interval estimate is (0.3132, 0.3768), so we can expect the number to be between 313 and 377 passengers.

To determine the interval estimate of the number of passengers that you would expect to carry more than one piece of luggage on the plane, we can use the formula for the confidence interval for a proportion. First, we calculate the sample proportion of passengers carrying more than one bag, which is 345/1000 = 0.345. Then, we find the standard error using SE = sqrt(p(1-p)/n), where p is the sample proportion and n is the sample size. Substituting the values, we get SE = sqrt(0.345(1-0.345)/1000) = 0.0162.

Next, we find the margin of error by multiplying the standard error by the critical value for the desired level of confidence. Since the problem does not specify a level of confidence, we will use a 95% confidence level, which corresponds to a critical value of 1.96. The margin of error is therefore 1.96 * 0.0162 = 0.0318.

Finally, we construct the confidence interval by subtracting and adding the margin of error from the sample proportion. The interval estimate is given by (0.345 - 0.0318, 0.345 + 0.0318), which simplifies to (0.3132, 0.3768). Therefore, we can expect the number of passengers carrying more than one piece of luggage on the plane to be between 313 and 377.

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Answer:

Step-by-step explanation:

From the given right angle triangle,

The unknown side represents the hypotenuse of the right angle triangle.

With m∠40 as the reference angle,

x represents the adjacent side of the right angle triangle.

4 represents the opposite side of the right angle triangle.

To determine x, we would apply

the Tangent trigonometric ratio.

Sin θ = opposite side/hypotenuse. Therefore,

Tan 40 = 4/x

x = 4/Tan 40 = 4/0.839

x = 4.8

Answer:

The answer to your question is the last option

Step-by-step explanation:

Process

1.- To calculate the rate of change, calculate slope

Formula

             m = (y2 - y1) / (x2 - x1)

x1 = 1           y1 = 1200

x2 = 2         y2 = 2400

2.- Substitution

             m = (2400 - 1200) / (2 - 1)

3.- Simplification

             m = 1200 / 1

4.- Result

             m = 1200 meters / minute

Answer:

(d) 1200 Meters per minute

Step-by-step explanation:

hope it helps you!!!!!

Answer: 59106

Step-by-step explanation:

We would apply the formula for exponential decay which is expressed as

A = P(1 - r)^ t

Where

A represents the population after t years.

t represents the number of years.

P represents the initial population.

r represents rate of growth.

From the information given,

P = 60000

r = 0.1% = 0.1/100 = 0.001

t = 2015 - 2000 = 15 years

Therefore

A = 60000(1 - 0.001)^15

A = 60000(0.999)^15

A = 59106

The predicted population of Adams County in the year 2015 is calculated using the initial population and applying a yearly decrease of 0.1% over 15 years, resulting in approximately 59,106 residents.

The question involves calculating the predicted population of Adams County in the year 2015 based on a yearly decrease of 0.1% from the year 2000.

To find the population in 2015, we need to apply the percentage decrease for each year from 2000 to 2015, which is a total of 15 years. The formula to calculate the population after a certain number of years with a consistent percentage change is: [tex]P = P_0 (1 - r)^t[/tex] where P is the final population, P₀ is the initial population, r is the rate of decrease, and t is the number of years.

Using the given data, P0 = 60,000, r = 0.001 (0.1% expressed as a decimal), and t = 15 years.

So, the calculation will be: P = 60,000 (1 - 0.001)¹⁵ = 60,000 (0.999)¹⁵ = 60,000 (0.985075) ≈ 59,106

Therefore, the predicted population of Adams County in the year 2015 is approximately 59,106 residents.

Answer:

  -7x +7y -z = 16

Step-by-step explanation:

We can define the function ...

  F(x, y, z) = f(x, y) -z

and differentiate at the point (x, y, z) = (2, 5, 5) to get ...

  fx(2, 5, 5) = -7 . . . . given

  fy(2, 5, 5) = 7 . . . . given

  fz(2, 5, 5) = -1 . . . . partial derivative of the above equation

Then the equation of the plane can be written as ...

  fx(x -2) +fy(y -5) +fz(z -5) = 0

  -7(x -2) +7(y -5) -1(z -5) = 0 . . . . . substitute for fx, fy, fz

  -7x +14 +7y -35 -z +5 = 0 . . . . . eliminate parentheses

  -7x +7y -z = 16 . . . . equation of the tangent plane

Answer: They are away for [tex]2\dfrac{3}{4}\ hours[/tex] from home.

Step-by-step explanation:

Since we have given that

Time to get there = [tex]\dfrac{1}{4}[/tex]

Time to get back = [tex]\dfrac{1}{4}[/tex]

Number of soccer games = 3

Time for each soccer games = [tex]\dfrac{3}{4}[/tex]

So, total time for 3 games would be

[tex]3\times \dfrac{3}{4}=\dfrac{9}{4}[/tex]

So, the time for which they will be away from home is given by

[tex]\dfrac{1}{4}+\dfrac{9}{4}+\dfrac{1}4}=\dfrac{1+9+1}{4}=\dfrac{11}{4}=2\dfrac{3}{4}\ hours[/tex]

Hence, they are away for [tex]2\dfrac{3}{4}\ hours[/tex] from home.

Caleb and his family will be away from home for a total of 2 3/4 hours.

To find out how long Caleb and his family will be away from home, we need to calculate the total time for the trip to and from the soccer games, as well as the duration of the games.

Adding it all together:

Total driving time: 1/4 hour + 1/4 hour = 1/2 hour

Total game time: 2 1/4 hours

Total time away from home: 1/2 hour + 2 1/4 hours = 2 3/4 hours

Therefore, Caleb and his family will be away from home for a total of 2 3/4 hours.

Answer:

27 days

Step-by-step explanation:

There is a total of 90 days in the semester, and she bought lunch 30% of the total days, then the total number of days she brought the lunch is 27 days.

The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other terms, it is a relationship where the worth of the entire is always considered to be 100.

As per the information provided in the question,

Total days in the semester = 90

Margaret comes with lunch, 30% of the total days.

So, in total days, Margaret comes with lunch,

D = 90 × 30/100

D = 2700/100

D = 27 days.

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Answer:

C

Step-by-step explanation:

A function is a special kind of relation in which each valid input gives exactly one output.

C {(22, 10), (23, 10), (24, 7), (25, 5)}

So C is the correct option.

Answer:

Step-by-step explanation:

Answer

She plans to collect 350 dollars

Step-by-step explanation:

Knowing that 245 dollars is equal to only 70% of what Rachel hopes to collect, the equation:

70% * x = 245

where x = money she plans to collect in total, is applicable,

Solving:

70/100 * x = 245,

7/10 * x =245,

7x/10 = 245,

7x = 2450,

x = 350 dollars

Answer:

A.

Step-by-step explanation:

The problem states that -3 is our y-intercept, so (0,-3) must be one of the answer choices. Next, just graph the equation to find the other two coordinate pairs are (1,-1) and (2,1).

Answer:

Perimeter ΔRON = 18.66 units

Step-by-step explanation:

Complete Question has these information given as well:

Now, we draw an image according to the information given. THe image drawn is attached.

Looking at the figure, we can say the perimeter of triangle RON would be:

RON = OR + ON + RN

We know according to tangent theorem, QN = QR

RN is equal to that as well and RN = [tex]5\sqrt{3}[/tex]

Now,

OR and ON is the radius, which is "5"

Perimeter of RON = 5 + 5 + [tex]5\sqrt{3}[/tex] = 10 + [tex]5\sqrt{3}[/tex] = 18.66 units

Perimeter ΔRON = 18.66 units

Answer:

18.7 units

Step-by-step explanation:

Answer:

1/4 or 25%

Step-by-step explanation:

The set of new shoes is composed by all pairs bought by either Harry or Kate.

Harry bought a pair of rain boots and a pair of tennis shoes while Kate got a pair of tennis shoes and sandals, totaling 4 pairs. Out of those 4 pairs, only 1 pair are rain boots, the fraction corresponding to rain boots is:

[tex]f = \frac{1}{4}=25\%[/tex]

Rain boots are 1/4 of the set of new shoes.

The value of John's silver collection changes at a faster rate than the value of John's baseball card collection.

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

It is a relation of the form y = aˣ  in mathematics, where x is the independent variable

The exponential function is given in the question

V = 500(1.05)^2t + 600(0.95)^t

Every 6 months, t = 2t

The value of John's silver collection changes =  500(1.05)²ˣ⁶ = 897.928

The value of  baseball card collection =  600(0.95)⁶ = 441.055

Thus, the value of John's silver collection changes at a faster rate than the value of John's baseball card collection.

Learn more about exponential function here:

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The question seems to be incomplete the correct question would be

The value of John's baseball card collection decreases exponentially over time, and the value of his silver collection increases exponentially over time. If the value of John's two collections combined t years from now is given by the function V = 500(1.05)^2t + 600(0.95)^t, which statement must be true?

A) John's silver collection is more valuable currency than his baseball collection.

B) The value of John's silver collection changes at a faster rate than the value of John's baseball card collection.

C) John's baseball card collection decreases in value by 10% every six months.

D) The total value of the two collections remains constant over time.

Answer:

  17 cm

Step-by-step explanation:

The formula for the area of a parallelogram is ...

  A = bh

The base (b) is given as (5 cm +15 cm) = 20 cm. The area is given as 340 cm^2. Filling in the give numbers, we have ...

  340 cm^2 = (20 cm)h

Dividing by the coefficient of h gives ...

  (340 cm^2)/(20 cm) = h = 17 cm

The height of the parallelogram is 17 cm.

_____

Comment on the geometry

The triangles at either end of the figure will be 5-12-13 right triangles, meaning the height of the figure is 12 cm. Using that height, we find the area to be (12 cm)(20 cm) = 240 cm^2 (not 340 cm^2). This leads us to believe there is a typo in the problem statement.

As the problem is given, the geometry is impossible. The height of the parallelogram cannot be greater than the length of the slanted side.

As the problem is written, it is a "one-step" problem. (Divide the area by the base length.) If the area were not given, then the Pythagorean theorem would be required to find the height. That is a 2-step problem:

  13^2 = 5^2 + h^2

  h^2 = 169 -25 = 144 . . . . solve for h²

  h = √144 = 12 . . . . . . . . . take the square root

It is not at all clear what 3 steps you're supposed to show in your work.