A man wishes to have a rectangular shaped garden in his backyard. He has 84 feet of fencing with which to enclose his garden. a) Write an expression for the perimeter of the garden. b) The area of the garden is A = l*w. Use the perimeter equation from part (a) to write the area in terms of just one variable. c) Find the dimensions for the largest area garden he can have if he uses all the fencing.

Answer:

downtown workers

Step-by-step explanation:

The research group should do the survey with downtown workers in order to find the opinions for the construction of a new downtown parking garage in downtown. Since the workers need to commute to downtown for work by various modes such as buses, private vehicles, bicycles, taxis, share vehicles, etc., therefore the the research group will get maximum useful information from the downtown workers for the construction of a new parking garage.

Thus, option "downtown workers" is correct.

The population of the survey would be the city residents.

The population of the survey would be the city residents. The research group wants to find the opinions of the city residents on the construction of a new downtown parking garage. While downtown shoppers, visitors, and workers could provide valuable insights, the opinions of the city residents would be the most relevant and encompassing for understanding the overall impact of the new downtown parking garage.

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Answer:

C. Band is the most popular elective among juniors.

Step-by-step explanation:

Let's just arrange your table:

                   Art      Band      Choir      Drama      Total

Juniors:     0.02      0.27        0.24       0.05        0.58

Seniors:     0.12      0.04       0.05       0.21         0.42

Total:         0.14       0.31         0.29        0.26          1

What you see here are portions or percentages of the people who chose under each category.

Here's another way to look at it.

                   Art      Band      Choir      Drama      Total

Juniors:        2%      27%        24%        5%           58%

Seniors:       12%      4%           5%         21%         42%

Total:            14%      31%        29%        26%   100%

If you read it horizontally, you are looking at it based on Juniors and Seniors.

If you read it vertically, you're looking at it based on the elective class.

The totals show how the group looks as a whole. And it gives you an idea of how much of the population chose each elective class.

Let's go back to your choices.

A is wrong, because as you can see, only 12% of the population that are Seniors chose Art. The most popular was actually Drama with 21%.

B. Is wrong as well because  only 5% of the population that are seniors chose Choir.

C. Is true because the as you can see, 27% of the population that are juniors chose Band.

D is wrong because of the above statement.

Now you do not have to make them into percentages to do this. You can also interpret the same thing by looking for the highest relative frequency to determine which one is most popular.

Answer:

C. Band is the most popular elective.

Step-by-step explanation:

Answer:

The domain of the function is 0 ≤ h ≤ 50

Independent and dependent variables are h and g respectively.

Step-by-step explanation:

Given function that shows the volume of the water,

[tex]V=121\pi h[/tex]

Where, h represents the height of water ( in meters ) filled on the water tank,

Since, the height can not be negative,

⇒ 0 ≤ h,

Also, the height of the tower is 50 m,

That is, h can not exceed 50,

⇒ h ≤ 50

By combining the inequalities,

0 ≤ h ≤ 50,

Domain of the given function is the set of all possible value of h,

Hence, Domain for the given function is 0 ≤ h ≤ 50

Now, the variable which is taken for measuring the another variable is called independent variable while the variable which is obtained by independent variable is called dependent  variable,

Here, we take different values of h for finding the different values of g,

Therefore, independent and dependent variables are h and g respectively.

Answer:

  b.  x^2 +2cx +bc+ac-ab = 0

Step-by-step explanation:

It's a matter of what I would describe as tedious algebra. You have to multiply by the least common denominator, then simplify to standard form.

After multiplying the equation by (x+a)(x+b)(x+c) and subtracting the right side, you have ...

  (x +b)(x +c) +(x +a)(x +c) -(x +a)(x +b) = 0

Expanding each factor pair gives ...

  (x² +(b+c)x +bc) +(x² +(a+c)x +ac) -(x² +(a+b)x +ab) = 0

Collecting terms gives ...

  x²(1 +1 -1) +x(b+c +a+c -a -b) +(bc +ac -ab) = 0

  x² +2cx +bc +ac -ab = 0 . . . . . matches selection B

The greatest number of students that could be in each row is 12, which is the greatest common divisor of 36 and 120. The color guard will have 3 rows, and the high school marching band will have 10 rows.

To determine the greatest number of students that could be in each row and the number of rows each group will have, we need to find the greatest common divisor (GCD) of the two numbers representing the members in each group, 36 and 120. The greatest common divisor is the largest number that divides both numbers without leaving a remainder. Calculate this by listing the factors of each number or using the Euclidean algorithm.

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
The greatest common divisor is the largest factor both numbers share, which is 12. Therefore, the greatest number of students per row is 12.

Now, to find the number of rows for each group, divide the total number of members in each group by the number of students per row:

So, there will be 3 rows of color guard members and 10 rows of marching band members.

Answer:

  1050 g < weight ≤ 1150 g

Step-by-step explanation:

Let w represent the weight of the package in grams. The the number of 100-gram increments after the first 250 grams is given by ...

  ⌈(w-250)/100⌉ . . . . . . . where ⌈ ⌉ signifies the ceiling function

and the charges for a package exceeding 250 grams will be ...

  0.65 + 0.10⌈(w -250)/100⌉ = 1.55

  0.10⌈(w -250)/100⌉ = 0.90 . . . . . . . . subtract 0.65

  ⌈(w -250)/100⌉ = 9 . . . . . . . . . . . . . . . divide by 0.10

  8 < (w-250)/100 ≤ 9 . . . . . . . . . . . . . . meaning of ceiling function

  800 < w -250 ≤ 900 . . . . . . . . . . . . . multiply by 100

  1050 < w ≤ 1150 . . . . . . . . . . . . . . . . . add 250

The weight in grams could be greater than 1050 and at most 1150 for a charge of $1.55.

Answer:

x² + y² = 42.25

Step-by-step explanation:

The equation of a circle centred at the origin is

x² + y² = r² ← r is the radius

here r = 6.5, hence

x² + y² = 6.5², that is

x² + y² = 42.25 ← equation of circle

Answer: [tex]x^2 + y^2 = 42.25[/tex]

Step-by-step explanation:

The equation of a circle in center-radius form is:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

Where the center is at the point (h, k) and the radius is "r".

Given the circle with radius 6.5 and centered at the origin, you can identify that:

 [tex]h=0\\y=0\\r=6.5[/tex]

Then, substituting values into [tex](x - h)^2 + (y - k)^2 = r^2[/tex], you get:

[tex](x - 0)^2 + (y - 0)^2 = (6.25)^2[/tex]

[tex]x^2 + y^2 = 42.25[/tex]

Problem: Same y intercept as x+4y=16, through (4,5)

Y intercept is when x=0 so 4y=16, y=4, y intercept (0,4)

Slope of line through (0,4) and (4,5) is change in y over change in x,

m = (5 - 4)/(4 - 0) = 1/4

Answer: slope 1/4

Check:

The new line is y = (1/4) x + 4

because the y intercept is still (0,4)

Let's check it's through (4,5)

(1/4) (4) + 4 = 5 check

Rounded to the nearest hundredth of a percent, the probability that both chosen people own a dog is approximately 1.44%.

We have,

The probability of the first person owning a dog is 12%, or 0.12.

Given that the first person owns a dog, the probability of the second person also owning a dog (assuming independence) remains 12%, or 0.12.

To find the probability that both of them own a dog, you multiply these probabilities:

Probability = 0.12 * 0.12 = 0.0144

To express this as a percentage, multiply by 100:

Probability = 0.0144 * 100 = 1.44%

Thus,

Rounded to the nearest hundredth of a percent, the probability that both chosen people own a dog is approximately 1.44%.

Learn more about probability here:

https://brainly.com/question/14099682

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The probability that both randomly chosen people own a dog is 1.44%.

To find the probability that both randomly chosen people own a dog, we multiply the probability that the first person owns a dog by the probability that the second person also owns a dog.

Given:

- Probability that a person owns a dog [tex]\( P(\text{dog}) = 12\% = 0.12 \)[/tex]

Since the events (ownership of dogs by two different people) are independent, we use the multiplication rule for independent events.

[tex]\[ P(\text{both own a dog}) = P(\text{person 1 owns a dog}) \times P(\text{person 2 owns a dog}) \][/tex]

[tex]\[ P(\text{both own a dog}) = 0.12 \times 0.12 \][/tex]

[tex]\[ P(\text{both own a dog}) = 0.0144 \][/tex]

Now, convert the decimal to a percentage:

[tex]\[ P(\text{both own a dog}) = 0.0144 \times 100\% = 1.44\% \][/tex]

Answer:

Heres the truth.

Step-by-step explanation:

If you haven't learned anything and you need to do a DBA. Just tell your teacher this, "Even though I've completed the Module... I still don't fully understand the concepts throughout the module. Is there anyway you can help me go over, review, and workout specific things that i understand and don't understand?"

It's best to actually do the work instead of submiting questions for others to answer on here. You should ask for help from a teacher, or go to the online tutoring.

Answer:

255 milliliters.

Step-by-step explanation:

The fraction of Compound A in the mixture = 3 / (3+ 5) = 3/8.

So the amount of A to make 680 mls of the drug

= (3/8) * 680

=  255 milliliters.

Answer:

44°

Step-by-step explanation:

The arc of DC in degrees is the same as the angle of DOC. So it is 44°

Answer:

If plants infested with aphids are sprayed with diluted coffee then the aphids will die.

Step-by-step explanation:

"Aphids sprayed with diluted coffee will not infest the plants" doesn't explain what happens to the aphids. (For example: they die, etc.)

"Plant sprayed with diluted coffee will not be infested by aphids" doesn't explain why it will not be infested by aphids.

"If plants with bug infestations are sprayed with diluted coffee then the bugs will die" doesn't say what type of bug, not all bugs will die from diluted coffee on plants.

The hypothesis best suited for Amy's test is 'If plants infested with aphids are sprayed with diluted coffee then the aphids will die', because it directly tests the claim Amy read online and is measurable through an experiment.

The appropriate hypothesis for Amy to test in order to determine whether spraying plants with diluted coffee will kill aphids is: 'If plants infested with aphids are sprayed with diluted coffee then the aphids will die'.

This hypothesis directly addresses the question Amy has and can be tested through an experiment where plants infested with aphids are sprayed with a diluted coffee solution. If the aphids die after being sprayed, the hypothesis would be supported. Conversely, if the aphids do not die, the hypothesis would need to be revised.

https://brainly.in/question/47679077

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Answer:

Step-by-step explanation:

h(0) = -.01·0² +3·0 = 0 . . . . . the height when the ball was hit

The function can be factored as ...

  f(d) = -0.01d(d -300)

This has zeros at d=0 and d=300, so the maximum will be halfway between, at d=150.

  f(150) = -0.01·150(150 -300) = -1.5(-150) = 225

The height of the ball when hit was 0 feet, and the ball reached a maximum height of 225 feet.

Bryan hits a golf ball whose path is given by the function f(d) = -0.01d2 + 3d, where d is the distance the ball travelled in feet and f(d) is the height of the ball. The height of the golf ball when it was hit was feet and the ball reached a maximum height of feet.

x = amount of liters of the 15% OJ

y = amount of liters of the 5% OJ

let's recall that

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}[/tex]

so then, the amount of juice in the 15% solution will be (15/100)*x, or 0.15x

and the amount of juice in the 5% solution will be (5/100)*y or 0.05y.

we know our mixture must be 10 liters at 14% or namely 14/100, which will give in juice (14/100)*10 or 1.4 liters or pure juice in the solution with water making the OJ.

[tex]\bf \begin{array}{lcccl} &\stackrel{liters}{quantity}&\stackrel{\textit{\% of }}{juice}&\stackrel{\textit{liters of }}{juice}\\ \cline{2-4}&\\ \textit{15\% OJ}&x&0.15&0.15x\\ \textit{5\% OJ}&y&0.05&0.05y\\ \cline{2-4}&\\ mixture&10&0.14&1.4 \end{array}~\hfill \begin{cases} x+y=10\\ \boxed{y}=10-x\\ \cline{1-1} 0.15x+0.05y=1.4 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\textit{substituting on the 2nd equation}}{0.15x+0.05\left( \boxed{10-x} \right)}=1.4\implies 0.15x+0.5-0.05x=1.4 \\\\\\ 0.10x+0.5=1.4\implies 0.10x=0.9\implies x=\cfrac{0.9}{0.10}\implies \blacktriangleright x = 9 \blacktriangleleft \\\\\\ \stackrel{\textit{since we know that}}{y=10-x}\implies y=10-9\implies \blacktriangleright y=1 \blacktriangleleft[/tex]

Answer:

  one real root: n ≈ 2.38450287889

Step-by-step explanation:

My favorite solution method for higher-degree polynomials is to use a graphing calculator.

Descartes' rule of signs tells you the one sign change among coefficients means there will be one positive real root. A graph shows you it is about 2.4, hence irrational (not a divisor of 33, so not rational).

You can use a cubic formula to find an explicit expression for the root, or you can find its value using any of several iteration methods. The attachment shows Newton's method iteration being used to refine the graph value of 2.385 to the more accurate 2.38450287889.

__

Factoring that root from the cubic results in a quadratic with irrational coefficients. Its vertex form is approximately ...

  y = (n +2.692)² + 6.591

Hence, the complex roots will be near -2.692±i√6.591.

_____

There are formulas for the roots of a cubic. The formula tells you the real root for this cubic is ...

  n = 2√(2/3)cosh(1/3·arccosh(24√(3/2))) -1 ≈ 2.38450287889

Answer:

(s-6)/r

option D

Step-by-step explanation:

The slope-intercept form a line is y=mx+b where m is the slope and b is the y-intercept.

Compare y=mx+b and y=cx+6, we see that m=c and c is the slope.

Now we are also given that (r,s) is on our line which means s=c(r)+6.

We need to solve this for c to put c in terms of r and s as desired.

s=cr+6

Subtract 6 on both sides:

s-6=cr

Divide both sides by r:

(s-6)/r=c

The slope in terms of r and s is:

(s-6)/r.

Answer:

Period=6

Step-by-step explanation:

Given:

t=1cos(1.05h)+37

Using acos(bx-c)+d to find the period of the given function

amplitude= a

period= 2π/Bb

phase shift=c (positive is to the left)

vertical shift=d

comparing with t=1cos(1.05h)+37, we get

a=1

b=1.05

c=0

d=37

period= 2π/b

          =2π/1.05

          =5.983

          =6

Period of function is 6, after every 6 hours the refrigerator sensor will reach its maximum temperature and the cycle will move towards reducing temperature i.e it'll reach the minimum temperature then again the cycle will move upwards raising the temperature to maximum and so one period will be completed!

Answer:

6

Step-by-step explanation:

Felicity set the thermostat of her refrigerator to 37°F. The refrigerator temperature t in degrees Fahrenheit h hours after the temperature sensor in the refrigerator is activated satisfies t=1cos(1.05h)+37. Therefore, the period of the function is 6.

Answer:

(140, 37)

Step-by-step explanation:

If we are looking for the point where the 2 companies charge the same amount, we need to set the 2 cost function equal to each other and solve for the number of miles that makes the cost the same.  The number of miles will also be the same at this cost.  That means we need cost functions for each.  x is the number of miles that is driven, our independent variable.  If A-1 charges .10 per mile, the expression is .1x.  If the flat fee is 23, regardless of how many miles you drive, you can expect to pay

y = .1x + 23

If EZ charges .05 per mile, the expression is .05x.  If the flat fee is 30, regardless of how many miles you drive, you can expect to pay

y = .05x + 30

If we want to see where the cost functions are equal, we set the right sides of those equations equal to one another and solve for the number of miles that makes the cost the same.

.1x + 23 = .05x + 30 and

.05x = 7 so

x = 140 miles.

In order to find the cost we will pick one of the equations and sub in 140 for x and solve for y.

y = .1(140) + 23

y = 14 + 23

y = 37

The coordinate pair is (140 miles, $37)

This means that at 140 miles driven, the cost is $37 no matter which rental agency you choose.

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

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

We have:

[tex]f(x)=3x+6\to m_f=3[/tex]

From the table:

[tex](1,\ 3),\ (2,\ 6)\\\\m_g=\dfrac{6-3}{2-1}=\dfrac{3}{1}=3[/tex]

[tex]m_f=m_g=3[/tex]

Answer:

1st one

Step-by-step explanation:

Answer:

x=6/cos(72) is the exact answer.

[tex]x \approx 19.416[/tex].

Step-by-step explanation:

Sine

opposite

hypotenuse

Cosine

adjacent

hypotenuse

Tangent

opposite

adjacent

Soh Cah Toa is an abbreviation used to help remember the trigonometric ratios.

We see we have the angle measurement 72 degrees given at the bottom. I'm going to label my sides with respect to that angle.

The hypotenuse is x.

The adjacent is 6.

We don't have anything about the opposite side but we don't need it to find x.

So anyways we have this:

The hypotenuse is x and

the adjacent is 6.

If you look at the ratios we want to use cosine.

[tex]\cos(72)=\frac{6}{x}[/tex]

or

[tex]\frac{\cos(72)}{1}=\frac{6}{x}[/tex]

We are going to cross multiply.

x cos(72)=1 (6)

cos(72) * x=6

Now we are going to divide both sides by cos(72) giving us:

x=6/cos(72)

x=6/cos(72) is the exact answer.

Let's put it into our calculator now:

[tex]x \approx 19.416[/tex].

Answer:

6

Step-by-step explanation:

The 8 is the leading coefficient, the -7 is the linear term, and the 6 is the constant.

Answer:

the constant term is 6.

Second option is correct.

Step-by-step explanation:

The quadratic function is [tex]f(x)=8x^2-7x+6[/tex]

The general form of a quadratic function is [tex]y=ax^2+bx+c[/tex]

Here c is the constant term and a can't be zero.

On comparing the given equation with the general form, we get

a = 8

b = -7

c = 6

Therefore, the constant term is 6.

Second option is correct.

Answer:

D

Step-by-step explanation:

15-x=4

Subtract 15 from both sides

leaves you with

-x=-11

x=11

Hey there! :)

15 - x = 4

Subtract 15 from both sides.

-x = 4 - 15

Simplify.

-x = -11

Divide both sides by -1.

-x ÷ -1 = -11 ÷ -1

x = 11

Therefore, your answer is D. 11

~Hope I helped! :)

Answer:

Option D RX=4 units

Step-by-step explanation:

we know that

In the right triangle RTS

The cosine of angle TRS is equal to

cos(TRS)=RT/RS

substitute

cos(TRS)=6/9 -----> equation A

In the right triangle RTX

The cosine of angle TRX is equal to

cos(TRX)=RX/RT

substitute

cos(TRX)=RX/6 -----> equation B

∠TRS=∠TRX -----> is the same angle

Match equation A and equation B

6/9=RX/6

RX=6*6/9=4 units

Answer:

Ntoine and Tess have a disagreement over how to compute a 15% gratuity on $46.00.

This in real becomes :

[tex]0.15\times46=6.90[/tex] dollars

But, Tess  says, "It is easy to find 10% of 46 by moving the decimal point one place to the left to get $4.60. Do that twice. Then add the two amounts to get $4.60 + $4.60 = $9.20

So, Tess is wrong. Rather she should have done 10% of $46 giving $4.6 and then half of 4.6 that is 2.3 dollars. Getting a total of [tex]4.6+2.3=6.9[/tex] dollars which is the real amount.

Answer:

Ntoine and Tess have a disagreement over how to compute a 15% gratuity on $46.00.

This in real becomes :

dollars

But, Tess  says, "It is easy to find 10% of 46 by moving the decimal point one place to the left to get $4.60. Do that twice. Then add the two amounts to get $4.60 + $4.60 = $9.20

So, Tess is wrong. Rather she should have done 10% of $46 giving $4.6 and then half of 4.6 that is 2.3 dollars. Getting a total of  dollars which is the real amount.

Step-by-step explanation:

trust me

Joan makes $275/week.

In addition to $275, she also makes 4 percent on sales over $1000.

So, 1250 - 1000 = 250.

Then 250(0.04) = 10.

Let t = amount of her paycheck for the week.

t = $275 + $10

t = $285

Answer:

By continuing my education I increased my earning potential from $21,484 to $39,746 a year. That's a difference of $18262 a year.

If the additional education costs $18,000, then in one year it will pay for itself.

Answer:

The answer is 1 year.

Step-by-step explanation:

You increased your yearly earning potential from $21,484 to $39,746.

The difference is : [tex]39746-21484=18262[/tex] dollars

This difference is in a year.

So, if the additional education costs $18,000, then in about 1 year it will pay for itself.

Hence, the answer is 1 year.

Answer:

2÷ 4

Step-by-step explanation:

Quotient means division

2÷ 4