A farmer wants to build a rectangular pen with 80 feet of fencing. The pen will be built against the wall of the barn, so one side of the rectangle won't need a fence. What dimensions will maximize the area of the pen? Find length and width.

Answer:

14/x+3

Step-by-step explanation:

The system of equation for the following conditions contains equation the equations: x + y ≤ 30 and 9x + 15y 240.

What is system of equation?

A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A set of equations satisfied by the same set of variables is called a system of linear equations."

Let the hours Alisa work for lawn mowing job is "x" hours and for coaching job is "y" hours.

As given in the question, Alisa can work at most 30 hours.

So the total working hours should be equal or less that 30 hours.

Therefore, the first equation can be written as:

x + y ≤ 30

And it is also given that, she needs to earn at least $240, while Her lawn mowing job pays $9 an hour, and her coaching job pays $15 for an hour.

So, Total earning = per hour earning x total hour

lawn mowing job earning = 9(x)

coaching job earning = 15(y)

Therefore, the second equation can be written as:

9x + 15y 240

Hence, the system of equation is: x + y ≤ 30 and 9x + 15y 240

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The value of variable x is 16.5 using the cross-multiplication method.

The denominator of the first term is multiplied by the numerator of the second term when utilizing the cross-multiplication method.

In mathematics, more specifically in elementary arithmetic and elementary algebra, one could cross-multiply an equation between two fractions or rational expressions to make the equation easier or to determine the value of a variable.

So, the value of x will be:

Use the cross-multiplication method as follows:

2x-7/4 = x+3/3

3(2x-7) = 4(x+3)

6x - 21 = 4x + 12

2x = 12 + 21

2x = 33

x = 33/2

x = 16.5

Therefore, the value of variable x is 16.5 using the cross-multiplication method.

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Correct question:
Obtain the value of x.

99% confidence Interval for the mean number of hours a student studies per week is (21.0208,18.9792)

Given:

mean x = 20

standard deviation σ = 3.5

sample size n = 78

z score for 99% = 2.576

Interval = x±z*s/[tex]\sqrt{n}[/tex]

= 20±2.576*3.5/[tex]\sqrt{78}[/tex]

= 20±2.576*0.39629

= 20±1.0208

Interval = (21.0208,18.9792)

Therefore 99% confidence Interval for the mean number of hours a student studies per week is (21.0208,18.9792).

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The number of displays are possible is 3

Total number of species Lightning bugs = 69

We have to arrange the same number of Lightning bugs in each row

First find the factors of the number 69

The factors of 69 = 1, 3, 23, 69

First combination is (1 × 69)

Arrange 1 Lightning bug in each row, then the number of rows will be 69

(3 × 23)

Arrange 3 Lightning bugs in each rows, then the number or rows will be 23

(23 × 3)

Arrange 23 Lightning bugs in each rows, then the number of rows will be 3

Hence, the number of displays are possible is 3

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The equation that can be used to find the side length of the shape is 14s - 7s/2 = 84

From the information, the two sides of the rectangle are 14 and s.

Area of a rectangle = length × width

The triangle is cut from the rectangle, the height is s/2 and the base is 14.

The area will be: = 1/2 × base × height

= 1/2 × 14 × s/2

= 7s/2

The area of shaded part will be;

= Area of rectangle - Area of triangle

= 14s - 7s/2

Since area is 84, the equation is 14s - 7s/2 = 84.

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Answer: 26

Step-by-step explanation:

1. Make an equation

n+n+2+n+4=78

(You have n+2 because to get to the next even number you'd have to add 2. For example, 2 is even, to get to the next even number, 4, you have you add 2.)

2. Combine like terms

3n+6=78

3. Solve for n

3n=72

n=24

4. Solve for the second number

(The second number would be n+2)\

n+2

24+2

26

ANSWER: 26

Answer:

A. 63.

Step-by-step explanation:

There is no null hypothesis in this situation there is no differences in the opinions about marriage between men and women

In the field of science, hypothesis testing is an effective method of determining whether or not there is a relationship between two or more variables. A null hypothesis is a default position or a general statement that no relationship or connection exists between the given variables.

The hypothesis is then tested, and based on the results of the tests, a conclusion is drawn either approving or rejecting the null hypothesis.

In the given situation, where the researcher predicted that women would have different opinions about marriage than men, the null hypothesis could be formulated because there is no difference in the opinions of men and women about marriage.

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By using ratio, it is calculated that John have 42 sweets.

What is ratio?

Ratio between two quantity tells us how much bigger is one quantity as compared to the other quantity.

The first part of the ratio is called antecedent and the second part of the ratio is called consequent

Vicky and John share some sweets in the ratio 2:7

Let Vick shares 2x sweets and John shares 7x sweets

Vicky ends up with 12 sweets

By the problem,

[tex]2x = 12\\x = \frac{12}{2}\\x = 6[/tex]

Number of sweets John have = [tex]7 \times 6 = 42[/tex]

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Answer:

Marcy got 16 wrong.

Step-by-step explanation:

You simply multiply 1 ( from the missed side of the ratio ) by 4 ( how many Marcy got wrong ) which equals 4. Then you do the same to the other side. 4 ( from the "correct" side of the ratio ) by 4 ( how many Marcy got wrong ). 4 x 4 is 16. So, Marcy got 16 wrong.

Answer:

16

Step-by-step explanation:

The ratio is 1:4 means for 1 wrong word, she got 4 words correct. If she has 4 words wrong, multiply that with 4 and you got 16.

Answer: B

Step-by-step explanation:

To rewrite the expression 12x+8 to find an equivalent expression.

The answer is

 12 x + 8 is equivalent to 4(3x + 2) is equivalent to  

 3x + 3x+3x+3x + 2 +2+2+2 is  equivalent to (x+x+x)+(x+x+x)+(x+x+x)+(x+x+x)+2+2+2+2

Therefore these are the possible expressions

Step: 1

Here given that,

Rewrite the expression 12x + 8 to find an equivalent expression. Show three possible expressions. What do the rewritten expressions tell you about the relationships among the quantities.

Step: 2

When you rewrite an expression, you are writing an equivalent expression. 

 12 x + 8 is equivalent to 4(3x + 2) is equivalent to  

 3x + 3x+3x+3x + 2 +2+2+2 is equivalent to  

(x+x+x)+(x+x+x)+(x+x+x)+(x+x+x)+2+2+2+2

Therefore these are the possible expressions

Hence the answer is

 12 x + 8 is equivalent to 4(3x + 2) is equivalent to  

 3x + 3x+3x+3x + 2 +2+2+2 is equivalent to  

(x+x+x)+(x+x+x)+(x+x+x)+(x+x+x)+2+2+2+2

Therefore these are the possible expressions

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If t=1, then d=3:  In 1 minute, the snail traveled 3 inches.

If t=2, then d=6:  In 2 minutes, the snail traveled 6 inches.

If t=3, then d=9:  In 3 minute, the snail traveled 9 inches.

The snails speed is 3 inches per minute.  That's what the 3 represents.  The change in distance (inches) for each minute that passes.

Answer:

Step-by-step explanation:

When adding or subtracting, the matrices must be the same size!

Therefore, B-A is not possible.

The slope of a line parallel to the line whose equation is 10x + 6y = -96 is;

m = - 5/3

Find the slope fully simplify my answer.

10x + 6y =-96

y = - 5/3 x – 16

y = - 5/3 x + (-16)

y = - 5/3 x + (-16), m = - 5/3

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Answer: 10

Step-by-step explanation: it’s 10 because 2 is a multiple of 10 and 10 is 10 so no change required.

Answer:

LCD = 10

Step-by-step explanation:

7/2 = 35/10

3/10 = 3/10

The probability of choosing the biased coin if you win a prize is 0.3056

To answer this query, we employ the conditional probability formula. It is, where

P(B|A) is the likelihood that event B will occur in the absence of event A.

is the likelihood that both A and B will occur.

P(A) denotes the likelihood that A will occur.

The following probability applies:

50% chance of winning a prize with the fair coin.

There is a 100-78 = 22% chance of winning a reward with the biased coin.

50% chance of selecting each coin.

What is the likelihood that you would choose the biased coin if you were to win a prize?

Event A: Receiving the award

Choosing the skewed coin is event B.

the likelihood of selecting the skewed coin and obtaining the reward.

p(A∩B) = 0.5 * 0.22 = 0.11

probability of winning the prize:

p(A) = 0.5*0.22 + 0.5 *0.5 = 0.36

conditional probability:

p(B/A) = 0.11/0.36= 0.3056

the probability of choosing the biased coin if you win a prize is 0.3056

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If n is an integer , the possible values of n in the given inequality are n > 5/2 and  n < 10       .

In the question ,

it is given that ,

the inequality is 5 < 2n < 20 , where n is an integer .

we need to find the all the possible values of n that satisfy the given inequalities .

to find the possible values of n , we solve both sides of the inequality separately ,

that is ,

5 < 2n

dividing both sides in the inequality by 2, we get

5/2 < n

n > 5/2

and

2n < 20

dividing both sides in the inequality by 2 , we get

n < 20/2

n < 10

Therefore , the possible values of n are n > 5/2 and  n < 10   .

The given question is incomplete , the complete question is

Write down all the possible values of n for the inequality 5<2n<20 , where n is an integer ?

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The probability that the frog will escape without being eaten by the snake is [tex]\frac{63}{146}[/tex]

What is Markov Process?

A Markov chain or Markov process is a stochastic model that depicts a series of potential occurrences where each event's likelihood is solely determined by the state it reached in the preceding event.

First, take notice that the frog has a probability of 1/2 of finally being eaten by the snake once it is on pad 5, and a probability of 1/2 of eventually emerging from the pond unharmed. Therefore, all that needs to be determined is the probability that the frog on pad 1 will make it to pad 5 without being eaten.

Consider the frog’s jumps in pairs. The frog on pad 1 will advance to pad 3 with probability [tex]\frac{9}{10} \frac{8}{10}[/tex][tex]=\frac{72}{100}[/tex] will be back at pad 1 with probability [tex]\frac{9}{10} \frac{2}{10}[/tex][tex]=\frac{18\\}{100}[/tex]

s

[tex]\frac{72}{100}[/tex] ÷  [tex](\frac{72}{100}+\frac{10}{100} )=\frac{36}{41}[/tex]   and the probability that it ultimately makes it to pad 0 is [tex]\frac{10}{100}[/tex] ÷ [tex](\frac{72}{100}+\frac{10}{100} )=\frac{5}{41}[/tex].Similarly, in a pair of jumps the frog will advance from pad 3 to pad 5 with probability [tex]\frac{7}{10} \frac{6}{10} =\frac{42}{100}[/tex], will be back at pad 3 with probability [tex]\frac{7}{10} \frac{4}{10} +\frac{3}{10} \frac{8}{10} =\frac{52}{100}[/tex].

Because the frog will ultimately make it to pad 5 or pad 1 from pad 3, the probability that it ultimately makes it to pad 5 is [tex]\frac{42}{100}[/tex] ÷ [tex]( \frac{42}{100} +\frac{6}{100} )=\frac{7}{8}[/tex] and the probability that it ultimately makes it to pad 1 is [tex]\frac{6}{100}[/tex] ÷ [tex](\frac{42}{100} +\frac{6}{100} )=\frac{1}{8}[/tex]

The series of steps that must be made in pairs for the frog to get to pad 5 without being eaten is

1 → 3 → 5, 1 → 3 → 1 → 3 → 5, 1 → 3 → 1 → 3 → 1 → 3 → 5 and so on.

The sum of the respective probabilities of reaching pad 5 is then

[tex]\frac{36}{41} \frac{7}{8} +\frac{36}{41} \frac{1}{8} \frac{36}{41} \frac{7}{8}+\frac{36}{41} \frac{1}{8} \frac{36}{41} \frac{1}{8} \frac{36}{41} \frac{7}{8}+.....[/tex]

[tex]= \frac{63}{82} (1+\frac{9}{82} +(\frac{9}{82})^{2} +....)[/tex]

[tex]=\frac{63}{82}[/tex]÷[tex](1-\frac{9}{82} )[/tex]

[tex]= \frac{63}{73}[/tex]

Therefore the requested probability is [tex]\frac{1}{2}\frac{63}{73} = \frac{63}{146}[/tex]

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Answer:

Left bottom graph is the correct one.

Answer: The bottom left graph

Step-by-step explanation: The top two are decreasing, so you can rule those answers out. The bottom right one is increasing by more than 4, so that wouldn’t be the answer either. That leaves you with one option which fits the description of the graph.

The values of x and y are not in a linear relationship.

Given,

x y

1 4.3

2 8.6

3 12.9

4 16.3

The linear relationship between x and y can be determined by using,

[tex]y=kx\\k=\frac{y}{x}[/tex]

Where, k=constant rate of change

If k is same for all values of x and y then the given data are said to be in linear relationship.

At first row,

[tex]k=\frac{4.3}{1} =4.3[/tex]

At second row,

[tex]k=\frac{8.6}{2}=4.3[/tex]

At third row,

[tex]k=\frac{12.9}{3}=4.3[/tex]

At fourth row,

[tex]k=\frac{16.3}{4} =4.075[/tex]

So, the k is not same for all values for x and y. Hence, the given data is non linear

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The angles in the figure are:

∠PQR = 45°

∠POR = 90°

Given : O is the centre of circle, ∠OPQ = 25° and ∠ ORQ = 20°

To Find : ​values of ∠ POR and ∠ PQR.

OP = OQ  = Radius

⇒ ∠OPQ = ∠OQP  

⇒ ∠OQP = 25°

OR = OQ  = Radius

⇒ ∠OQR = ∠ORQ

⇒ ∠OQR = 20°

∠PQR = ∠OQP + ∠OQR

⇒ ∠PQR =   25° + 20°

⇒ ∠PQR =   45°

∠POR = 2∠PQR

⇒ ∠POR = 2*45°

⇒  ∠POR = 90°

Hence we get the two angles as 45° and 90° respectively.

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Answer:   p = 9 - 0.5s

Optionally you can replace 0.5 with the fraction 1/2

===================================================

Explanation:

s = number of slices

0.5s = total width of all of those slices mentioned

9-0.5s = amount left over.

For example, if he eats s = 4 slices then he has eaten 0.5s = 0.5*4 = 2 inches of bread, and there are 9-2 = 7 inches left.

Notice how 9-0.5s=9-0.5*4 = 9-2 = 7.

The equation p = 9 - 0.5s is not an inverse variation because it's not in the form p = k/s, where k is some constant.

The value of the car to be, to the nearest cent, after 11 years is $7641.

Given data;

A brand-new car is bought for $20300. The car's value decreases by 9.5% annually.

To know the value of the car to be, to the nearest cent, after 11 years;

[tex]S(t) = 20300*(0.915)^t[/tex]

[tex]S(11) = 20300*(0.915)^1^1[/tex]

[tex]S(11) = 20300*0.376[/tex]

[tex]S(11) = 7640.61[/tex]

Hence, the value of the car after 11 years is $7641.

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Answer:

I believe it would be 300 dollars per week, I hope this was right :)

Step-by-step explanation:

.4x750=300

Answer:

simplify - 3x^2xy-(-3x^2) x 2x ^3y^2^z: -3x^3y+6x^2+3y2z

Answer:

42

Step-by-step explanation:

1.25x = 52.5  Divide both sides by 1.25

x = 42