Forty minutes of hot yoga and 10 minutes of jumping jacks burns 510 calories. Thirty minutes at hot yoga and 20 minutes of jumping jacks burns 470 calories. How many calories are burned per minute of yoga? How many calories are burned per minute of jumping jacks

The dimensions for the plot that would enclose the most area are a length and a width of 125 feet.

In this question we shall use the first and second derivative tests to determine the optimal dimensions of a rectangular plot of land. The perimeter ([tex]p[/tex]), in feet, and the area of the rectangular plot ([tex]A[/tex]), in square feet, of land are described below:

[tex]p = 2\cdot (w+l)[/tex] (1)

[tex]A = w\cdot l[/tex] (2)

Where:

In addition, the cost of fencing of the rectangular plot ([tex]C[/tex]), in monetary units, is:

[tex]C = c\cdot p[/tex] (3)

Where [tex]c[/tex] is the fencing unit cost, in monetary units per foot.

Now we apply (2) and (3) in (1):

[tex]p = 2\cdot \left(\frac{A}{l}+l \right)[/tex]

[tex]\frac{C}{c} = 2\cdot (\frac{A}{l}+l )[/tex]

[tex]\frac{C\cdot l}{c} = 2\cdot (A+l^{2})[/tex]

[tex]\frac{C\cdot l}{c}-2\cdot l^{2} = 2\cdot A[/tex]

[tex]\frac{C\cdot l}{2\cdot c} - l^{2} = A[/tex] (4)

We notice that fencing costs are directly proportional to the area to be fenced. Let suppose that cost is the maximum allowable and we proceed to perform the first and second derivative tests:

FDT

[tex]\frac{C}{2\cdot c}-2\cdot l = 0[/tex]

[tex]l = \frac{C}{4\cdot c}[/tex]

SDT

[tex]A'' = -2[/tex]

Which means that length leads to a maximum area.

If we know that [tex]c = 8[/tex] and [tex]C = 4000[/tex], then the dimensions of the rectangular plot of land are, respectively:

[tex]l = \frac{4000}{4\cdot (8)}[/tex]

[tex]l = 125\,ft[/tex]

[tex]A = \frac{(4000)\cdot (125)}{2\cdot (8)} -125^{2}[/tex]

[tex]A = 15625\,ft^{2}[/tex]

[tex]w = \frac{15625\,ft^{2}}{125\,ft}[/tex]

[tex]w = 125\,ft[/tex]

The dimensions for the plot that would enclose the most area are a length and a width of 125 feet.

We kindly invite to check this question on areas: https://brainly.com/question/11952845

Answer: She would've used 82 gallons

Answer:

it should be 60°. the single marks on each side means they are all equal

Answer:

m∠L=60º

Step-by-step explanation:

The triangle is an equilateral triangle meaning that all angles and sides are equal.

m∠L=60º

Hope this helps :)

Answer:324.24??? Not sure just a guess.

Step-by-step explanation:

Answer:

Applicants for the federal funding

Step-by-step explanation:

$60

Step-by-step explanation:

The unit rate can be determined by dividing $24 by 8 attendees to get

[tex]\dfrac{\$24}{8\:\text{attendees}} = \$3/\text{attendee}[/tex]

so when 20 people are attending the graduation picnic, his total cost is going to be

[tex]20\:\text{attendees}×\dfrac{\$3}{\text{attendee}} = \$60[/tex]

Answer:

1/2

Step-by-step explanation:

The dice has 6 faces therefore the probability that three will show is 3/6 which when divided gives you 1/2

Step-by-step explanation:

Check the picture below.

The number of groups that may make will be 5.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Maya utilized a drawing to partition 86 she made gatherings of 17 with 1 remaining over.

Then the number of the groups that may make will be given as,

⇒ (86 - 1) / 17

Simplify the expression, then we have

⇒ (86 - 1) / 17

⇒ 85 / 17

⇒ 5

The number of groups that may make will be 5.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ2

Answer:

x = about 2.705

Step-by-step explanation:

Does this help? Are you supposed to find x? That's what I did but you don't state what exactly you need.... So.....?

Answer:

28

Step-by-step explanation:

10 - (-18)

=> 10 + 18

=> 28

Hoped this helped.

Answer:

10 - (-18)

= 10 + 18

= 28

Step-by-step explanation:

Answer:

the answer is 7

Step-by-step explanation:

Using the normal distribution, it is found that the percentage of people spend between 41 and 56 minutes watching TV shows on this streaming service is:

a) 13.5%

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem:

The proportion between 41 and 56 minutes is the p-value of Z when X = 56 subtracted by the p-value of Z when X = 41, hence:

X = 56:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{56 - 71}{15}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a p-value of 0.16

X = 41:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{41 - 71}{15}[/tex]

[tex]Z = -2[/tex]

[tex]Z = -2[/tex] has a p-value of 0.025

0.16 - 0.025 = 0.135

0.135 x 100% = 13.5%

Hence option a is correct.

A similar problem is given at https://brainly.com/question/25769446

Answer:

f+3

incresed means +

Answer:

The expression for 'f increased by 3' will be f+3.

Step-by-step explanation:

This means that 3 will be added to 'f'. Since, 'f' is a variable and '3' is a numeral, therefore they cannot be added. The expression for it will be f+3.

Have a great day! :D

Answer:

20 servings of 100-milliliter sports drink

Step-by-step explanation:

Answer:Full wall is 6 times 1/6 (6*1/6=1), so 6 times half a gallon, or 3 gallons.

Step-by-step explanation:

Answer:

4.30 naira

Step-by-step explanation:

Splitting in half, we have that they both get 3.60 naira each. Adding 70 kobo to 3.60 naira, we have 4.30 naira. Since we need Tayo's share to be 70 kobo more than Bisi's, we give Tayo the bigger share and the left cash to Bisi (2.90 naira).

Tayo will get 3.95 more than the naira of the given shares.

In mathematics, an expression is a combination of numbers, variables, and operators (such as addition, subtraction, multiplication, and division) that can be evaluated to obtain a value.

Let's call the amount that Visit gets "x".

According to the problem, Tayo gets 70 kobos (0.70 nairas) more than Visit. So, Tayo gets:

x + 0.70

The total amount of money shared between them is 7.20 naira. So, we can set up an equation:

x + (x + 0.70) = 7.20

Simplifying this equation, we get:

2x + 0.70 = 7.20

Subtracting 0.70 from both sides, we get:

2x = 6.50

Dividing both sides by 2, we get:

x = 3.25

To find out how much Tayo gets, we can use the equation we came up with earlier:

x + 0.70

Substituting x = 3.25, we get:

3.25 + 0.70 = 3.95

Therefore, Tayo will get 3.95 more than the naira.

To know more about an expression follow

https://brainly.com/question/723406

#SPJ2

Answer:

16,32,16

Step-by-step explanation:

We can see that there is a pattern in this ratio table- 4, 8, 12. I can assume that the next number will be 16, beucase 4+4=8, 8+4=12, 12+4=16.  For the apple juice, we just follow the same pattern as for the orange juice, by adding the number by itself, so the patttern is 8, 16,24, 32.

Answer:

X=11/5

Step-by-step explanation:

Hope your cheating is nice

Answer:

[tex]x=\cfrac{11}{5}[/tex]

Step-by-step explanation:

[tex]25+30=15x+10x\\15x+10x=25+30\\25x=25+30\\25x=55\\\cfrac{25x}{25}=\cfrac{55}{25}\\x=\cfrac{11}{5}[/tex]

Step-by-step explanation:

Reduce 24/96 to lowest terms

Find the GCD (or HCF) of numerator and denominator. GCD of 24 and 96 is 24.

24 ÷ 2496 ÷ 24.

Reduced fraction: 14. Therefore, 24/96 simplified to lowest terms is 1/4.

Step-by-step explanation:

Here is an Explanation

Reduce 24/96 to lowest terms

The simplest form of

24

96

is

1

4

.

Steps to simplifying fractions

Find the GCD (or HCF) of numerator and denominator

GCD of 24 and 96 is 24

Divide both the numerator and denominator by the GCD

24 ÷ 24

96 ÷ 24

Reduced fraction:

1

4

Therefore, 24/96 simplified to lowest terms is 1/4.

Answer:

14 m actural sif 124075n

Step-by-step explanation:

Answer:

second or last

Step-by-step explanation:

Answer:  1/8 < 2/5 < 5/7

Step-by-step explanation:

Answer:

33.6

Step-by-step explanation:

This problem is a multiplication problem.

=> 4.8 x 7

=> 33.6

Therefore, the solution to 4.8 x 7 is 33.6.

The problem 4.8 x 7 is a multiplication problem. The solution to 4.8 x 7 is 33.6.

Here, we have,

given that,

The problem 4.8 x 7 is a multiplication problem.

To solve it, we multiply 4.8 by 7.

4.8 x 7

Therefore, the answer to the problem 4.8 x 7

This problem is a multiplication problem.

=> 4.8 x 7

=> 33.6

Therefore, the solution to 4.8 x 7 is 33.6.

To learn more on multiplication click:

brainly.com/question/5992872

#SPJ6

Answer:

Length is 50ft, width is 160ft

Step-by-step explanation:

Answer:

-9/4

also known as

-2  1/4

Step-by-step explanation:

(10-1)/(5-9) = 9/-4

parallel = same slope

Answer:

slope = - [tex]\frac{9}{4}[/tex]

Step-by-step explanation:

Calculate the slope m of line f using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (5, 10 ) and (x₂, y₂ ) = (9, 1 )

m = [tex]\frac{1-10}{9-5}[/tex] = [tex]\frac{-9}{4}[/tex] = - [tex]\frac{9}{4}[/tex]

Parallel lines have equal slopes , then

slope of line g = - [tex]\frac{9}{4}[/tex]

Answer:

The answer is seventeen (17)