Last year Mr Peterson had a fence all the way around his garden. He can reuse all of the fence he had around the garden last year but he needs to buy more fencing to go around this years garden. How many more meters of fencing is needed for this years garden than last years?

Answers

Answer 1

Complete Question:

Last year Mr. Petersen’s rectangular garden had a width of 5 meters and an area of 20 square meters.  This year he wants to make the garden three times as long and two times as wide.  

Last year, Mr. Petersen had a fence all the way around his garden. He can reuse all of the fence he had around the garden last year, but he needs to buy more fencing to go around this year’s garden.  

How many more meters of fencing is needed for this year’s garden than last year’s?

Answer:

26 meters of fencing needed

Step-by-step explanation:

Given

Last Year:

[tex]Width = 5m[/tex]

[tex]Area = 20m^2[/tex]

This Year:

[tex]Length = 3\ times\ longer[/tex]

[tex]Width = 2\ times\ wider[/tex]

Required

Determine how many more meters is needed

Represent last year's length of Fence with L and last year's width with W

First, we need to calculate L

[tex]Area = L * W[/tex]

Where

[tex]Area = 20m^2[/tex]

[tex]W = 5m[/tex]

[tex]20m^2 = L * 5m[/tex]

Divide both sides by 5m

[tex]\frac{20m^2}{5m} = \frac{L * 5m}{5m}[/tex]

[tex]\frac{20m^2}{5m} = L[/tex]

[tex]L = \frac{20m^2}{5m}[/tex]

[tex]L = 4m[/tex]

So, we have that:

For Last Year

[tex]Length = 4m[/tex] and [tex]Width = 5m[/tex]

For this year:

[tex]Length = 3\ times\ longer[/tex]

[tex]Length = 3 * 4m[/tex]

[tex]Length = 12m[/tex]

[tex]Width = 2\ times\ wider[/tex]

[tex]Width = 2 * 5m[/tex]

[tex]Width = 10m[/tex]

So, for this year, we have:

[tex]Length = 12m[/tex] and [tex]Width = 10m[/tex]

Next, we calculate perimeter of fencing in both years.

[tex]Perimeter = 2 * (Length + Width)[/tex]

Last Year:

[tex]Perimeter = 2 * (4m + 5m)[/tex]

[tex]Perimeter = 2 * 9m[/tex]

[tex]Perimeter = 18m[/tex]

This Year:

[tex]Perimeter = 2 * (12m + 10m)[/tex]

[tex]Perimeter = 2 * 22m[/tex]

[tex]Perimeter = 44m[/tex]

To get the meters of fencing needed this year, we simply calculate the difference in the calculated perimeters.

[tex]Difference = 44m - 18m[/tex]

[tex]Difference = 26m[/tex]

Hence, there are 26 meters of fencing needed


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It is assumed that the test results for a class follow a normal distribution with a mean of 78 and a standard deviation of 36. If you know that a student's grade is greater than 72, what is the probability that it is greater than 84? What do I know? What do I want to find out? What do we expect the answer to be? How do I go from what I know to what I want to find? Does this answer seem reasonable?

Answers

Answer:

0.7143

- You know the minimum possible grade of the student

- You want to find out the probability that that grade which is greater than 72 is also greater than 84

- Expect the answer to be 0.7143

- The explanation/steps is given below

- The answer seems (and is) reasonable. You only created a new lower limit.

Step-by-step explanation:

Distribution Type: Normal

Mean: 78

Standard deviation: 36

Range of marks: [78 - 36], [78 + 36]  = [42 to 114]

If you know that a student's grade is greater than 72, what is the probability that it's greater than 84?

In this case, the full probability level is between 72 and the upper limit of 114 (instead of between 42 and 114). First, find the fraction of this probability.

[114 - 72] ÷ [114 - 42]  = 42/72  = 0.5833

So, the probability of a student's mark falling between 72 and 114 is 0.5833.

Now making this a whole interval, 114 - 72 = 42

What fraction of this interval of 42 will bear marks between 84 and 114?

[114 - 84]  = 30

30/42  = 0.7143

Because of the first part of the question "If you know (are sure) that a student's grade is greater than 72...", your answer stops at 0.7143, since 72 was used as the lower limit.

5. Juliet has swimming lessons every 5th day and dance lessons every 3rd day. If she
had a swimming lesson and a dance lesson on October 1, when will be the next
date on which she has both swimming and dance lessons?
A. October 5
B. October 10 C. October 15 D. October 18

Answers

Hope this helps!

C. October 15

If i had 127 tables and each table could fit 4 people how many people could i seat?

Answers

You would have 31 with equal groups

The weight of eggs from a local farm are Normally distributed with mean of 2.1 ounces and a standard deviation of 0.25 ounces.

A graph titled Weight of Eggs has ounces on the x-axis going from 1.35 to 2.85 in increments of 0.25. The highest point of the curve is at 2.1. Everything to the left of that point and under the curve is labeled average, everything to the right is large.

An egg that weighs 2.0 ounces or more is labeled large and anything below is labeled average.

What percent of eggs from this farm are labeled as large? Round to the nearest tenth.

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Answer:

65.5

Step-by-step explanation:

Answer:

65.5

Step-by-step explanation:

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Answer:

False

Explanation

The x-intercept of a line occurs when the line intersects with the x-axis.

The population of a certain town is growing at a constant rate. Suppose the population is 1900 initially, and after 4 years the population is 2212. Which of these expresses the rate at which the population is increasing?

Answers

Answer:

The rate of change relates the change in population to the change in time.  The population increased by 2212−1900=312 people over the four-years.  To find the rate of change, divide the change in the number of people by the number of years.

2212−19004=3124

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So the population increased by 78 people per year.

Because we are told that the population increased, we would expect the slope to be positive.  This positive slope we calculated is therefore reasonable.

The midpoint of AB is M(6,-3). If the coordinates of A are (4, - 7), what are the
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Answers

Answer:

(8,1)

Step-by-step explanation:

(8,1) you have to add do to the same to B

Pont B is located at coordinates at the line AB (8, 1)

What are coordinates?

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

Given, The midpoint of AB is M(6,-3). If the coordinates of A are (4, - 7)

From the general formula of midpoints of a line

coordinates of midpoint = ((x₂ + x₁)/2, (y₂ + y₁)/2)

where,

(x₁, y₁) are the coordinates of A

(x₂, y₂) are the coordinates of B

And in our case Coordinates of the midpoint are (6, -3)

Thus,

6 = (4 + x₂)/2

x₂ = 8

-3 = (-7 + y₂)/2

y₂ = 1

therefore, the coordinates of Pont B at line AB are (8, 1)

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Can you help me please

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There is an attachment here. I hope it helps!!

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Answer:

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Step-by-step explanation:

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Find the equation of this line in slope intercept form y-2=1/2(x+8)

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Write the letters of the expressions that are equivalent to the given expression.
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Answers

Answer: A.) 10x + 15

Step-by-step explanation:

You would distribute (multiply) the 5 to the 2x which would then make it 10x and you would distribute (multiply) the 5 to the 3 which would then make it 15. Because the 5 is a positive number the sign stays the same.

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Answers

Answer:

375/1,000

Step-by-step explanation:

3/8=0.375

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For the following quadratic equation, find the discriminant.
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Answers

Answer:

d=-124

Step-by-step explanation:

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A researcher wishes to estimate within $5 the average repair cost of for a refrigerator. If she wishes to be 90% confident, how large of a sample would be necessary if the population standard deviation is $15.50?

Answers

Answer:

The sample size 'n' = 26

Step-by-step explanation:

Explanation:-

Given a researcher wishes to estimate within $5 the average repair cost of for a refrigerator

Given estimate "E" = $5

The  estimate within  the average is determined by

                [tex]E = \frac{Z_{0.10}S.D }{\sqrt{n} }[/tex]

 Level of significance    ∝ = 90 % or 10%

                                            = 0.90 or o.10

Z₀.₁₀ = 1.645

                                 [tex]E = \frac{Z_{0.10}S.D }{\sqrt{n} }[/tex]

                             [tex]5 = \frac{1.645 X15.50 }{\sqrt{n} }[/tex]

                        √n =  [tex]\frac{25.49}{5} = 5.099[/tex]

Squaring on both sides , we get

                        n = 26

Conclusion:-

The sample size 'n' = 26

Solve the given system of equations utilizing either the substitution or addition method.

Answers

Answer:

Value of x=4 and y=-13/3

Step-by-step explanation:

We need to solve the systems of equations

[tex]5x+3y=7 \ and \ \frac{3}{2}x-\frac{3}{4}y =9\frac{1}{4}[/tex]

Solving using substitution method:

Let:

[tex]5x+3y=7---eq(1) \\ \frac{3}{2}x-\frac{3}{4}y =9\frac{1}{4}---eq(2)[/tex]

Find value of x from eq(1) and put in eq(2)

[tex]5x+3y=7\\5x=7-3y\\x=\frac{7-3y}{5}[/tex]

Put value of x in eq(2)

[tex]\frac{3}{2}(\frac{7-3y}{5}) -\frac{3}{4}y =\frac{37}{4}\\\frac{21-9y}{10} -\frac{3}{4}y =\frac{37}{4}\\Taking \ LCM\\\frac{21*2-9y*2-3y*5}{20} =\frac{37}{4}\\\frac{42-18y-15y}{20} =\frac{37}{4}\\42-33y=\frac{37}{4}*20\\42-33y=185\\-33y=185-42\\-33y=143\\y=\frac{143}{-33}\\y=-\frac{13}{3}[/tex]

Now, finding value of x by putting value of y in eq(1)

[tex]x=\frac{7-3y}{5}\\x= \frac{7-3(-\frac{13}{3}) }{5}\\x=\frac{7+13}{5}\\x=\frac{20}{5}\\x=4[/tex]

So, Value of x=4 and y=-13/3

Your classmate tells you the details of the great deal he got on his mortgage: 30-year 1.1% fixed rate with a 20% down payment

If his new home costs $136,000, what is his down payment?

Answers

Answer:

27200

Step-by-step explanation:

Tina wants to buy a bouquet
of red roses. The original price
is $24. How much will Tina PAY
if she buys it during the sale
when it is 25% off?

Answers

Answer:

18

Step-by-step explanation:

If we know she will have a 25% discount, we know she will only pay 75%. So you divide by 4 and get 6. So now, If we subtract 25% (6), our 75% will be 18.

Answer:

It's 18

Step-by-step explanation:

25 percent of 24 is 6 dollars, subtract 6 from 24, you get 18, your welcome :D

Given that 3x – tan y = 4, what is dy/dx in terms of y?

Answers

Answer:

[tex]\frac{dy}{dx}[/tex] = 3 cos² y ⇒ B

Step-by-step explanation:

3x - tan(y) = 4

∵ The differentiation of tan(y) with respect to x is sec² y · dy/dx

∵ The differentiation of 3x with respect to x is 3

∵ the differentiation to 4 with respect to x is 0

∴ d/dx [3x - tan(y) = 4] is 3 - sec² y · dy/dx = 0

3 - sec²(y) · dy/dx = 0

→ Subtract 3 from both sides

∴ - sec² y · dy/dx = -3

→ Divide both sides by -1

∴ sec² y · dy/dx = 3

→ Divide both sides by sec²(x)

∴ [tex]\frac{dy}{dx}=\frac{3}{sec^{2}y}[/tex]

→ Remember [tex]\frac{1}{secy}[/tex] = cos y

∵ [tex]\frac{1}{sec^{2}y}[/tex] = cos² y

∴  [tex]\frac{3}{sec^{2}y}[/tex] = 3 cos² y

[tex]\frac{dy}{dx}[/tex] = 3 cos² y

dy/dx of 3x – tan y = 4 in terms of y is;

dy/dx = 3cos²y

We are given;

3x - tan y = 4

Let's differentiate in terms of y to get;

3 - sec²y(dy/dx) = 0

This is because the derivative of tan y in terms of y is sec²y(dy/dx).

Thus, using addition property of equality, we have;

3 = sec²y(dy/dx)

Now, in trigonometric ratios;

sec y = 1/cos y

Thus;

sec²y = 1/cos²y

Therefore;

3 = (1/cos²y) (dy/dx)

Thus;

dy/dx = 3cos²y

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is 16-7=4+5 true, false, or open?

Answers

Answer:

open

Step-by-step explanation:

Answer:

This is True.

Step-by-step explanation:

16-7=9

5+4=9

same ting

A student finds a positive correlation between the number of beds in a home and the number of plates in the kitchen.

Which variable is most likely the lurking variable that explains the correlation?




A: height of tallest person in the home

B: age of oldest person in the home

C: number of children in the home

D: number of pets in the home

im not doing great in math and i really need some help with this

Answers

C. The number of people in the home. This is because the more people in the house, more people are eating and using plates and there are going to be more beds for everyone to sleep on.

Answer:

here you go this is for confirmation

Step-by-step explanation:

Which statement about residual plots is NOT true?
A. The vertical axis shows residuals.
B. If there is an obvious pattern, the model is probably reasonable.
C. The x-axis appears in the middle of the graph.
D. The sum of the residuals is 0.

Answers

Answer:

A is the correct answer

Step-by-step explanation:

The not correct statement about residual plot is If there is an obvious pattern, the model is probably reasonable.

What is a residual plot?

A residual plot shows the difference between the observed response and the fitted response values.

Given that, Which statement about residual plots is not true

In the given options,

If there is an obvious pattern, the model is probably reasonable, this option is not correct because, The pattern in the residual plot suggests that predictions based on the linear regression line will result in greater error as we move from left to right through the range of the explanatory variable.

So, it is not needed if there is an obvious pattern, then the model is probably reasonable,

Hence, the not correct statement about residual plot is If there is an obvious pattern, the model is probably reasonable.

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Which weighs more a backpack that weighs 9.5 kg grams or a case of water that weighs 16 pounds

Answers

Answer:

The backpack weighs more

Step-by-step explanation:

9.5kg = 20.94391 lbs

Answer:

a backpack that weighs 9.5kg

Step-by-step explanation:

kilogram (kg) is stated to be 2.2 times heavier than a pound

A meat inspector has randomly selected 30 packs of 95% lean beef. The sample resulted in a mean of 96.2% with a sample standard deviation of 0.8%. Calculate an upper prediction bound for the leanness of a new pack using a prediction level of 99%. Assume normality. The contents of seven similar containers of sulfuric acid are 9.8, 10.2, 10.4, 9.8,10.0, 10.2, and 9.6 liters. Find a 95% confidence interval for the mean contents of all such containers, assuming an approximately normal distribution.

Answers

Answer:

a

 The upper bound of the 99% prediction level is [tex] 98.2  [/tex]  

b

 The  95% confidence interval is [tex]9.7383 <  \mu < 10.2617 [/tex]

Step-by-step explanation:

Considering first question

From the question we are told that

   The sample size is  n  =  30  

   The sample mean is  [tex]\= x = 96.2\%[/tex]

   The standard deviation is [tex]s = 0.8\%[/tex]

Generally the degree of freedom is mathematically represented as

        [tex]df = n - 1[/tex]

=>      [tex]df = 30 - 1[/tex]

=>      [tex]df = 29[/tex]

From the question we are told the confidence level is  99% , hence the level of significance is    

      [tex]\alpha = (100 - 99 ) \%[/tex]

=>   [tex]\alpha = 0.01[/tex]

Generally from the t distribution table the critical value  of   at a degree of freedom of is  

   [tex]t_{\alpha , 29} = 2.462[/tex]

Generally the  99%  prediction level is mathematically represented as

      [tex]\= x \pm [(t_{\alpha  , df }) * s * (\sqrt{1 + \frac{1}{ n} } )}] [/tex]

Generally the upper bound of the 99%  prediction level is mathematically represented as

      [tex]\= x + [(t_{\alpha  , df }) * s * (\sqrt{1 + \frac{1}{ n} } )}] [/tex]  

=>    [tex] 96.2 + (2.462 ) * 0.8 * (\sqrt{1 + \frac{1}{ 30} } )}] [/tex]  

=>    [tex] 98.2  [/tex]  

Considering second question

 Generally the sample is mathematically represented as

             [tex]\= x = \frac{\sum x_i}{n}[/tex]

=>           [tex]\= x = \frac{ 9.8 + 10.2 + \cdots +9.6 }{7}[/tex]  

=>           [tex]\= x = 10[/tex]    

Generally the standard deviation  is mathematically represented as

           [tex]\sigma = \sqrt{ \frac{ \sum ( x_ i - \= x)}{n-1} }[/tex]

=>        [tex]\sigma = \sqrt{ \frac{ ( 9.8 -10)^2 + ( 10.2 -10)^2 + \cdots + ( 9.6 -10)^2 }{7-1} }[/tex]

=>        [tex]\sigma = 0.283[/tex]

Generally the degree of freedom is mathematically represented as

      [tex] df =  n- 1 [/tex]

=>    [tex] df =  7- 1 [/tex]

=>    [tex] df =  6 [/tex]

From the question we are told the confidence level is  95% , hence the level of significance is    

      [tex]\alpha = (100 - 95 ) \%[/tex]

=>   [tex]\alpha = 0.05[/tex]

Generally from the t distribution table the critical value  of   at a degree of freedom of  is  

   [tex]t_{\frac{\alpha }{2} , 6 } =  2.447[/tex]

Generally the margin of error is mathematically represented as  

      [tex]E = t_{\frac{\alpha }{2} , 6 } *  \frac{\sigma }{\sqrt{n} }[/tex]

=>    [tex]E =2.447*    \frac{0.283 }{\sqrt{7} }[/tex]

=>    [tex]E =0.2617[/tex]

Generally 95% confidence interval is mathematically represented as  

      [tex]\= x -E <  \mu <  \=x  +E[/tex]

=>   [tex]10 -0.2617 <  \mu < 10 + 0.2617[/tex]

=>   [tex]9.7383 <  \mu < 10.2617 [/tex]

find the missing value of 6/9 = m/6​

Answers

Answer: 4

Step-by-step explanation:

6/9 = m/6  We can multiply both sides of the equation by 6 to solve for m

so we get 36/9 = m. m = 4

An african elephant in rhe wils will eat for as long as 16 hours each day. For how many hours does an elephant eat in one year? There are 365 days in one year.

Answers

Answer:

5840

Step-by-step explanation:

16 x 365 is 5840

Answer:

5,840

Step-by-step explanation:

16x365=?

16x365=5,840

Brainliest be good peeps Calculate the missing term in each
proportion.
2/11= /55
36/42= /
9/ = 21/28
6/9= /15

Answers

Answer:

1)  10

2) (not enough info) I got 6/7

3) 12

4) 10

Step-by-step explanation:

Find a GCF and find the numerator.

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