The organic garden at a restaurant is rectangular in shape and has a perimeter of 84 feet. If the length of the garden is 24 ft longer than the width of the garden what is the area of the garden in sq ft

Answers

Answer 1

Answer:

297 square feet

Step-by-step explanation:

Let w represent the width of the garden.

Since the length is 24 ft longer than the width, it can be represented by w + 24.

Use the perimeter formula, p = 2l + 2w. Plug in the perimeter and w + 24 as l, then solve for w:

p = 2l + 2w

84 = 2(w + 24) + 2w

84 = 2w + 48 + 2w

84 = 4w + 48

36 = 4w

9 = w

So, the width is 9 ft. Add 24 to this to find the length:

24 + 9 = 33

So, the length is 33 ft.

Find the area of the garden with the formula A = lw:

A = lw

A = (33)(9)

A = 297

The area of the garden is 297 square feet.


Related Questions

Match each equation with its number of unique solutions.
y = 3x2-6x+3
y = -x2 - 4x + 7
y = -2x2+9x-11
Two Real Solutions
One Real Solution
One Complex Solution
Two Complex Solutionse de

Answers

Answer:

y = 3x^2-6x+3    one real solution  

y = -x^2 - 4x + 7     two real solution

y = -2x^2+9x-11       two complex solutions

Step-by-step explanation:

b^2-4ac = 0   1 repeated real solution

b^2-4ac > 0   2 distinct real solutions

b^2-4ac < 0   2 complex solutions

The quadratic functions have the following solutions:

y = 3x²-6x+3 has two real solutions.

y = -x² - 4x + 7 has one real solution.

y = -2x²+9x-11 has one complex solution.

The given quadratic functions are y = 3x²-6x+3, y = -x² - 4x + 7 and y = -2x²+9x-11.

What is the discriminant of a quadratic equation?

The discriminant of a quadratic equation ax² + bx + c = 0 is in terms of its coefficients a, b, and c. i.e., Δ OR D = b² − 4ac.

Now, with the function y = 3x²-6x+3, we get

b² − 4ac=(-6)²-4×3×3=36-36=0

Since b=0 it has two real solutions.

Now, with the function y = -x² - 4x + 7, we get

b² − 4ac= (-4)²-4×(-1)×7=16+28=44

Since b>0 it has one real solutions.

Now, with the function y = -2x²+9x-11, we get

b² − 4ac= (9)²-4×(-2)×(-11)=81-88=-7

Since b<0 it has one complex solution.

Therefore, the quadratic functions have the following solutions:

y = 3x²-6x+3 has two real solutions.

y = -x² - 4x + 7 has one real solution.

y = -2x²+9x-11 has one complex solution.

To learn more about the quadratic function solutions visit:

https://brainly.com/question/1687230.

#SPJ2

Type the correct answer in each box. Use numerals instead of words.
What is the equation of the quadratic function shown in the graph?

Answers

Answer:

y - 8 = -2(x + 1)^2

Step-by-step explanation:

The vertex of this parabola is (-1, 8).  It opens downward, so the x^2 term has a negative coefficient.  The zeros are (-3, 0) and (1, 0), and the y-intercept is (0, 7).

Through the vertex form of the equation of a parabola we get:

y - (8) = a(x - (-1)) + 7, or

y - 8 = a(x + 1)^2.  Find coefficient a by substituting the coordinates (-3, 0) in this equation:

0 - 8 = a(-3 + 1)^2, or

-8 = a(-2)^2, or a = -2

The desired equation is

y - 8 = -2(x + 1)^2

In a recent health survey, 333 adult respondents reported a history of diabetes out of 3573 respondents. What is the critical value for a 90% confidence interval of the proportion of respondents who reported a history of diabetes

Answers

Answer:

The critical value for the 90% confidence interval is [tex]Z_c = 1.645[/tex].

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].

The critical value for the 90% confidence interval is [tex]Z_c = 1.645[/tex].

Does anyone know these?

Answers

Answer:

1 = - 4 - 14 √3

2 = 9 - 11 √3

Step-by-step explanation:

Question 1

(-4√3 + 2)(√3 + 4)

Apply FOIL method

= (-4√3) √3 + (-4√3) . 4 + 2 √3 + 2 . 4

Apply minus-plus rules: + (-a) = -a

= -4 √3 √3 - 4 . 4 √3 + 2 √3 + 2 . 4

Simplify

= - 4 - 14 √3

Question 2

(-3 + √3)(1 + 4 √3)

Apply FOIL method

= (-3) . 1 + (-3) . 4 √3 + √3 . 1 + √3 . 4 √3

Apply minus-plus rules: + (-a) = -a

= -3 . 1 - 3 . 4 √3 + 1 . √3 + 4 √3 √3

Simplify

= 9 - 11 √3

Find an equation of the line through these points (15,2.2) (5,1.6). Write answer in a slope-intercept form

Answers

Answer:

[tex]y=\frac{\displaystyle 3}{\displaystyle 50}x+\frac{\displaystyle 13}{\displaystyle 10}[/tex]

Step-by-step explanation:

Hi there!

Slope-intercept form: [tex]y=mx+b[/tex] where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept (the value of y when x is 0)

1) Determine the slope (m)

[tex]m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_1}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the given points (15,2.2) and (5,1.6):

[tex]m=\frac{\displaystyle 1.6-2.2}{\displaystyle 5-15}\\\\m=\frac{\displaystyle -0.6}{\displaystyle -10}\\\\m=\frac{\displaystyle 0.6}{\displaystyle 10}\\\\m=\frac{\displaystyle 0.3}{\displaystyle 5}\\\\m=\frac{\displaystyle 3}{\displaystyle 50}[/tex]

Therefore, the slope of the line is [tex]\frac{\displaystyle 3}{\displaystyle 50}[/tex]. Plug this into [tex]y=mx+b[/tex]:

[tex]y=\frac{\displaystyle 3}{\displaystyle 50}x+b[/tex]

2) Determine the y-intercept (b)

[tex]y=\frac{\displaystyle 3}{\displaystyle 50}x+b[/tex]

Plug in a given point and solve for b:

[tex]1.6=\frac{\displaystyle 3}{\displaystyle 50}(5)+b\\\\1.6=\frac{\displaystyle 3}{\displaystyle 10}+b\\\\1.6-\frac{\displaystyle 3}{\displaystyle 10}=\frac{\displaystyle 3}{\displaystyle 10}+b-\frac{\displaystyle 3}{\displaystyle 10}\\\\\frac{\displaystyle 13}{\displaystyle 10}=b[/tex]

Therefore, the y-intercept is [tex]\frac{\displaystyle 13}{\displaystyle 10}[/tex]. Plug this back into [tex]y=\frac{\displaystyle 3}{\displaystyle 50}x+b[/tex]:

[tex]y=\frac{\displaystyle 3}{\displaystyle 50}x+\frac{\displaystyle 13}{\displaystyle 10}[/tex]

I hope this helps!

Instructions: Complete the following theorem.



"If m⊥t and n⊥t, then

."

Answers

Answer:

m║n

Step-by-step explanation:

If two lines 'line m' and 'line n' are perpendicular to the 'line t', both the lines 'm' and 'n' will be parallel to each other.

If m ⊥ l and n ⊥ l, then m║n.

what is the relationship and what does X equal?
help! :)

Answers

Answer:

4x + 3 = 59

x = 14

Step-by-step explanation:

The vertical angles theorem states that when two lines intersect, the angles opposite each other are congruent. One can apply this here by stating the following:

4x + 3 = 59

Solve for (x), use inverse oeprations:

4x + 3= 59

4x = 56

x = 14

Answer:

Relationship : Vertical angle

Step-by-step explanation:

(4x + 3) = 59

4x = 59 - 3

4x = 56

x = 56/4

x = 14

0.45 0.40 0.11 This question uses the following probability model for the blood type of a randomly chosen person in the United States: Maria has type A blood. She can safely receive blood transfusions from people with blood types O and A. The probability that a randomly chosen American can donate blood to Maria is ______. (Give your answer to 2 decimal places.)

Answers

Answer:

[tex]P(O\ or\ A) = 0.85[/tex]

Step-by-step explanation:

Given

See attachment

Required

[tex]P(O\ or\ A)[/tex]

From the question, we understand that she can only get blood from O or A groups. So, the probability is represented as:

[tex]P(O\ or\ A)[/tex]

This is calculated as:

[tex]P(O\ or\ A) = P(O) + P(A)[/tex]

Using the American row i.e. the blood must come from an American.

We have:

[tex]P(O) = 0.45[/tex]

[tex]P(A) = 0.40[/tex]

So, we have:

[tex]P(O\ or\ A) = 0.45 + 0.40[/tex]

[tex]P(O\ or\ A) = 0.85[/tex]

What’s the answer to the question down below

Answers

Any linear equation can be written as

y = mx+b

where m is the slope and b is the y intercept

m = 1/2 in this case. It represents the idea that the snow fell at a rate of 1/2 inch per hour. In other words, the snow level went up 1/2 an inch each time an hour passed by.

b = 8 is the y intercept. It's the starting amount of snow. We start off with 8 inches of snow already.

The info "snow fell for 9 hours" doesn't appear to be relevant here.

The following box-and-whisker plots represent the fuel economy rates (combined city and highway) for the entire fleet
of two major car manufacturers.
Car Manufacturer B
Car Manufacturer A
+
5
0
10
40
45
50
15 20 25 30 35
Combined Fule Economy (in miles per gallon)
g
Which of the following statements is not true?
Car Manufacturer A's fleet has a larger range of fuel economy rates than Car Manufacturer B's fleet
The range of the middle half of the rates for both manufacturers is about the same
The median fuel economy rate of Car Manufacturer A is about 7 miles per gallon higher than the median fuel economy rate of Car
Manufacturer B
One of the vehicles in Car Manufacturer B's fleet has the lowest fuel economy rate of either manufacturer

Answers

Answer: Either C or D (explanation below)

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

Explanation:

Let's go through the answer choices to see which are true or which are false. The goal is to find which is false.

A) True. Notice the entire boxplot for fleet A is wider with its whiskers spanning out further compared to fleet B. Therefore, the range for set A is larger than the range of set B.B) True. This is an estimation and it appears the two boxes are the same width, so both seem to have the same IQR. Unfortunately, without the actual values of Q1 and Q3, it's impossible to confirm this 100%. C) False. The middle line in the box plot is the visual marker of the median. We see that the median of set A is less than the median of set B. So we found the answer and we could stop here. D) False. The min of car B's fleet is either at 15 or a little bit above it. Meanwhile, car A's minimum is well below 15 mpg. So saying that car B has the lowest fuel economy, for any car picked, compared to car A's fleet is incorrect.

Unfortunately, we found C and D to be false. So it's not clear if there's a typo or if your teacher meant to say something else.

20 students were asked “How many pets do you have in your household?” and the following data was collected:
2 1 0 3 1 2 1 3 4 0
0 2 2 0 1 1 0 1 0 1
Select the type of the data ?

Discrete

Continuous

Categorical

Qualitative
NO FAKE ANS
FRIST MARKED BRAINLIST
CHOOSE ONE ANS

Answers

Answer:

qualitative

Step-by-step explanation:

bcos the question is in quality format

Answer:

we are armysss!!!!\

hiiiiiiiiii

yoooooooo

heyyyyyy

brainlist meeee!

What is the solution of this equation 5( x - 4) = 3x + 4

Answers

5 (x - 4) = 3x + 4
5x - 20 = 3x + 4
5x - 3x = 4 + 20
2x = 24
x = 12

find m∠H
What does m∠H happened to equal​

Answers

Answer:

[tex]m\angle H = 30^o[/tex]

Step-by-step explanation:

Given

See attachment

Required

Find [tex]m\angle H[/tex]

To calculate [tex]m\angle H[/tex], we make use of:

[tex]\cos(\theta) = \frac{Adjacent}{Hypotenuse}[/tex]

So, we have:

[tex]\cos(H) = \frac{GH}{HI}[/tex]

This gives:

[tex]\cos(H) = \frac{10\sqrt3}{20}[/tex]

[tex]\cos(H) = \frac{\sqrt3}{2}[/tex]

Take arccos of both sides

[tex]m\angle H = cos^{-1}(\frac{\sqrt3}{2})[/tex]

[tex]m\angle H = 30^o[/tex]

Three ounces of cinnamon cost $2.40. If there are 16 ounces in 1 pound, how much does cinnamon cost per pound?

Answers

12.8$, you would divide 2.40 by 3 to get the cost per ounce. Then multiply that by 16 to get the cost for one pound.

Suppose we roll a pair of fair dice, let A=the numbers I rolled add up to exactly 8, and let B=the numbers I rolled multiply to an even number. Find P(Ac and Bc).

Answers

Answer:

P(Ac and Bc) = 7/36 = 0.1944 = 19.44%

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Possible outcomes:

For the pair of dice:

(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)

So 36 total outcomes.

Find P(Ac and Bc).

Complement of A(The result of the sum is different of 8) and complement of B(multiply to odd number). So the desired events are:

(1,1), (1,3), (1,5)

(3,1), (3,3)

(5,1), (5,5)

7 desired outcomes. So

P(Ac and Bc) = 7/36 = 0.1944 = 19.44%

Select all the correct answers.
Charles is reading about computers. He learns that a computer processor can perform one command in approximately 0.000000016
nanoseconds. What is this number expressed in scientific notation?
s
1.6E-8
1.6 x 10-7
1.6 x 10-8
1.6E-7
1.6 x 108
1.6E8
1.6 x 107
1.6E7
Next
Reset
82°F

Answers

9514 1404 393

Answer:

1.6×10^-81.6E-8

Step-by-step explanation:

The place value of a digit to the right of the decimal point is 10 to the negative power of the digit count. The 1st digit right of the decimal point has a place value of 10^-1.

Here, the most significant digit of 0.000000016 is in the 8th place to the right of the decimal point, so its place value is 10^-8.

  0.000000016 = 1.6×10^-8

Another way to write the same number is 1.6E-8. (The "E" is a stand-in for ×10^.)

_____

Your (graphing or scientific) calculator or a spreadsheet can display this in scientific notation for you.

__

That many nanoseconds, as this problem states, would be 1.6×10^-17 seconds. "Nano" is an SI prefix meaning 10^-9.

What is the value of the expression i 0 × i 1 × i 2 × i 3 × i 4?
1
–1
i
–i

Answers

Answer:

Answer is -1

Step-by-step explanation:

i1 = i 

i2 = -1 

i3 = -i

i4 = 1

i0 × i1 × i2 × i3 × i4 = 1 × i  × (- 1) × (- i) × 1 = i2 = - 1

Answer:the answer is -1

Step-by-step explanation:

Which of the following is equivalent to the expression below?
Square root of -81
A. 9
B. -9
C. 9i
D. -9i

Answers

Answer:

C 9i

D -9i

Step-by-step explanation:

sqrt(-81)

sqrt(81) sqrt(-1)

we know that sqrt(-1) = i

±9i

Norman and Suzanne own 35 shares of a fast food restaurant stock and 63 shares of a toy company stock. At the close of the markets on a particular day in​ 2004, their stock portfolio consisting of these two stocks was worth ​$1596.00. The closing price of the fast food restaurant stock was ​$19 more per share than the closing price of the toy company stock on that day. What was the closing price of each stock on that​ day? The price per share of the fast food restaurant stock is ​

Answers

Answer:

closing price of the fast food stock was $997.50

closing price of the toy company stock was $598.50

the price per fast food share was $28.50

Step-by-step explanation:

x = price per share fast food

y = price per share toy company

35x + 63y = 1596

x = y + 19

=>

35(y+19) + 63y = 1596

35y + 665 + 63y = 1596

98y + 665 = 1596

98y = 931

y = $9.50

=>

x = 9.5 + 19 = $28.50

the value of the whole fast food stock was

35x = 35×28.5 = $997.50

the cake if the whole toy company stock was

63y = 63×9.5 = $598.50

Safety regulations require that the time between airplane takeoffs (on the same runway) will be at least 2 minutes. When taking off, the run time of an airplane on the runway is 27 seconds. Planes are on average waiting 4 minutes and 21 seconds for take-off. On average there are 21 planes taking off per hour. How many planes are either on the runway or waiting to take off

Answers

Answer:

Number of planes on the runway or waiting to take off is approximately 2

Step-by-step explanation:

Given the data in the question;

On average there are 21 planes taking off per hour

rate of flow = frequency of take off = 21 planes / hr

= 21 planes per 60 minutes

= 0.35 planes/min

Now, we get the throughput time

throughput time = total time for take off =  waiting time on runway + run time on runway

= (4 minutes and 21 seconds) + 27 seconds

= 4.35 minutes + 0.45 minutes

= 4.8 minutes

Now, using Little's law;

Number of planes on the runway or waiting to take off will be;

N = Rate of flow × throughput time

we substitute

N = ( 0.35 planes/min ) × 4.8 min

N = 1.68 planes ≈ 2 planes

Therefore, Number of planes on the runway or waiting to take off is approximately 2

$32,520 divided by 30 people

Answers

Answer: $1,084 per person

Step-by-step explanation:

divide 32520 by 30

83
EDFN 1090/1092
Assignment 4
1. From statistics grades, John has a mean of 70 and Sx(standard deviation) of 15, Jane
has a mean of 70 and Sx(standard deviation) of 5. Hint: create a 68% Range)
Describe the two students in terms of consistency of their grades and give reason.

Answers

Answer:

68% of the time, John's grades will be between 55 and 85, while for Jane, 68% of the time, her grades will be between 65 and 75. They have the same mean grade, however, due to the lower standard deviation, Jane is more consistent, while John has the higher upside.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

John:

Mean of 70, standard deviation of 15.

70 - 15 = 55

70 + 15 = 85

68% of the time, John's grades will be between 55 and 85.

Jane:

Mean of 70, standard deviation of 5.

70 - 5 = 65

70 + 6 = 75.

68% of the time, Jane's grades will be between 65 and 75.

Describe the two students in terms of consistency of their grades and give reason.

68% of the time, John's grades will be between 55 and 85, while for Jane, 68% of the time, her grades will be between 65 and 75. They have the same mean grade, however, due to the lower standard deviation, Jane is more consistent, while John has the higher upside.

annual cost of 35,000 expected to save 40,000 during the first year how many months will the take to recover investment

Answers

Answer:

500000

Step-by-step explanation:

Can someone please do these three and number them? -Numbers: 10,11,12-

Answers

Answer:

10. Option: c11. Option: a12. Option: a

Help with question number one please

Answers

Answer:

165 hits

Step-by-step explanation:

27.5% of 600 is 600 x 27.5 / 100 = 165

If 1 kilogram (kg) is equal to about 2.2046 pounds (lbs.), what is the value of 1kg/2.2046lbs? What is the value of 2.2046lbs/1kg?

Answers

Step-by-step explanation:

The relation between kg and lbs is :

1 kg = 2.2046 lbs

We need to find the values of 1kg/2.2046lbs and 2.2046lbs/1kg.

So,

[tex]\dfrac{1\ kg}{2.2046\ lbs}=\dfrac{2.2046\ lbs}{2.2046\ lbs}\\\\=1[/tex]

and

[tex]\dfrac{2.2046\ lbs}{1\ kg}=\dfrac{2.2046\ lbs}{2.2046\ lbs}\\\\=1[/tex]

Hence, this is the required solution.

Answer:

Both are same as 1.

Step-by-step explanation:

1 kg = 2.2046 lbs

So,

[tex]\frac{1 kg}{2.2046 lbs }=\frac{1 kg }{1 kg} = 1[/tex]

And

[tex]\frac{2.2046 lbs}{1 kg }=\frac{1 kg }{1 kg} = 1[/tex]

convert decimal into fraction 17.38​

Answers

Answer:

869/50

Step-by-step explanation:

17.38

= 1738/100

= 869/50

PLEASE HELP

Complete the table to find the different combinations of coin quantities that have a sum of $2.41. (See photo above)

Answers

1) 56 pennies
2) 36 pennies
3) 14 dimes
4) 4 quarters
5) 5 nickels

Answer:

1st row 56 pennies

2nd row 36 pennies

3rd row 14 dimes

4th row 4 quarters

5th row 5 nickels

Step-by-step explanation:

1st row $1.85 + 56 cents = $2.41

2nd row $2.05 + 36 cents = $2.41

3rd row is $1.01 + $1.40 = $2.41

4th row $1.41 + $1.00 = 2.41

5th row $2.16 + 25 cents = $2.41

Urgent need answer for this one.

Answers

Answer:

4th option

Step-by-step explanation:

6/sin(65) = 5/sin(x)

or, 6×sin(x) = 5×sin(65)

or, sin(x) = 5×sin(65)/6

or, x = arcsin(5×sin(65)/6)

The length of a rectangle is 7cm less than 3 times it's width. It's area is 20 square cm. Find the dimensions of the rectangle

Answers

Answer:

4 cm by 5 cm (4 x 5)

Step-by-step explanation:

The area of a rectangle with length [tex]l[/tex] and width [tex]w[/tex] is given by [tex]A=lw[/tex]. Since the length of the rectangle is 7 less than 3 times its width, we can write the length as [tex]3w-7[/tex]. Therefore, substitute [tex]l=3w-7[/tex] into [tex]A=lw[/tex]:

[tex]A=lw,\\20=(3w-7)w[/tex]

Distribute:

[tex]20=3w^2-7w[/tex]

Subtract 20 from both sides:

[tex]3w^2-7w-20=0[/tex]

Factor:

[tex](w-4)(3w+5)=0,\\\begin{cases}w-4=0, w=\boxed{4},\\3w+5=0, 3w=-5, w=\boxed{-\frac{5}{3}}\end{cases}[/tex]

Since [tex]w=-\frac{5}{3}[/tex] is extraneous (our dimensions cannot be negative), our answer is [tex]w=4[/tex]. Thus, the length must be [tex]20=4l, l=\frac{20}{4}=\boxed{5}[/tex] and the dimension of the rectangle are 4 cm by 5 cm (4 x 5).

Other Questions
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