In which step does a mistake first occur? please help!
8÷2+(3x3-2)
Step 1: 8÷2+(3x1)
step 2: 8÷2+3
step 3: 4 +3
step 4: 7

The area of the park is 6,443,686,000 square meters

The green space per person is 100,683.91 square meters per person

No additional green space is required.

We have,

A)

To convert the area of the parks from acres to square meters, we multiply by the conversion factor:

= 1,591,000 acres x 4,046 square meters/acre

= 6,443,686,000 square meters

B)

To find the green space per person, we divide the total green space by the population:

green space per person = 6,443,686,000 square meters / 64,000 people

green space per person = 100,683.91 square meters/person

C)

Caldwell has more than the minimum requirement of 9 square meters per person.

To determine if it meets the suggested area of 50 square meters per person, we compare the calculated value to 50:

100,683.91 square meters/person > 50 square meters/person

green space per person = 100,683.91 square meters/person

So, Caldwell meets the suggested area of 50 square meters per person. No additional green space is required.

Thus,

The area of the park is 6,443,686,000 square meters

The green space per person is 100,683.91 square meters per person

No additional green space is required.

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Answer:

a. The length of the box = (40 - 2·x) cm

The height of the box = x cm

The width of the box = (25 - 2·x) cm

b. The formula for the volume of the box as a function of x is 4·x³ - 130·x² + 1000·x

c. The value of x that would maximize the volume of the box is x = 5 cm

d. The largest volume of the box is 2250 cm³

Step-by-step explanation:

a. The given parameters are;

The length of the cardboard = 40 cm

The width of the cardboard = 25 cm

The length of the box = (40 - 2·x) cm

The height of the box = x cm

The width of the box = (25 - 2·x) cm

b. The formula for the volume of the box = The area of the base of the box × Height of the box

The area of the base of the box =  (40 - 2·x) × (25 - 2·x) = 1000 - 80·x - 50·x + 4·x²

∴ The area of the base of the box = 4·x² - 130·x + 1000

The height of the box = x

The volume of the box = (4·x² - 130·x + 1000) × x = 4·x³ - 130·x² + 1000·x

The volume of the box in terms of x, V = 4·x³ - 130·x² + 1000·x

c. At the extremum point, dV/dx = 12·x² - 260·x + 1000 = 0

x = (260 ± √((-260)² - 4 × 12 × 1000))/(2 × 12)

x = (260 ± 140)/(24)

x = 5 or x = 16.\(\bar 6\)

At x = 5, the volume of the box is V = 4×5³ - 130×5² + 1000×5 = 2250

The volume of the box is V = 2250 cm³

At x = 16.67, the volume is 4×16.67³ - 130×16.67² + 1000×16.67 = -925.\(\overline {925}\)cm³

Therefore, the value of x that would maximize the volume of the box is x = 5 cm

d. The largest volume of the box is 4×(5 cm)³ - 130×(5 cm)² + 1000×(5 cm) = 2250 cm³.

Answer:

\(15\dfrac{39}{40} $ inches\)

Step-by-step explanation:

On the map, 3 inches = 10 miles in real life.

Therefore:

10 miles: 3 Inches

\(1$ miles rep $ \dfrac{3}{10}$ inches\)

If the real-life distance between two buildings is 53.25 miles

Distance on the map

\(\dfrac{3}{10}$ X 53.25 inches\\=15.975 inches\)

\(=15\dfrac{39}{40} $ inches\)

The distance between the two buildings on the map is therefore: \(15\dfrac{39}{40} $ inches\)

The approximate volume of the sphere is 6.01 ft³.

A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.

The volume of a sphere is expressed as:

Volume =  (4/3)πr³

Where r is the radius of the sphere and π is the mathematical constant pi (approximately equal to 3.14).

Given that the surface area of the sphere is 16 square feet.

First, we determine the radius r:

Surface area = 4πr²

Hence

16 = 4πr²

Dividing both sides by 4π, we get:

r² = 16/4πr

r = √( 16/4πr )

r = 1.128 ft

Plugging in the value of r that we just found, we get:

Volume =  (4/3)πr³

Volume =  (4/3) × 3.14 × (1.128 ft)³

Volume =  6.01 ft³

Therefore, teh volume is 6.01 ft³.

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Answer:

Step-by-step explanation:

The denominator is positive for any value of x.

So we solve the numerator:

The future value of the fund on January 1, 2018, just after the third deposit, is approximately $47,986.47.

To find the future value of the fund on January 1, 2018, just after the third deposit, we can use the compound interest formula:

\(FV = P(1 + r/n)^{nt}\)

Where:

FV = Future Value

P = Principal amount (initial investment)

r = Annual interest rate (expressed as a decimal)

n = Number of times the interest is compounded per year

t = Number of years

Let's calculate the future value step by step:

First deposit:

P = $16000

r = 7.2% = 0.072 (as a decimal)

n = 12 (compounded monthly)

t = 4.333 years (from September 1, 2010, to March 1, 2015)

\(FV_1 = 16000(1 + 0.072/12)^{(12*4.333)}\\= 16000(1 + 0.006)^{52}\\= 16000(1.006)^{52}\\= 20,296.43\)

Second deposit:

P = $13000

r = 7.2% = 0.072 (as a decimal)

n = 12 (compounded monthly)

t = 2.917 years (from March 1, 2015, to January 1, 2018)

\(FV_2 = 13000(1 + 0.072/12)^{(12*2.917)}\\= 13000(1 + 0.006)^{35}\\= 15,618.04\)

Third deposit:

P = $12000

r = 7.2% = 0.072 (as a decimal)

n = 12 (compounded monthly)

t = 0.084 years (from January 1, 2018, to January 1, 2018)

\(FV3 = 12000(1 + 0.072/12)^{(12*0.084)}\\= 12000(1 + 0.006)\\= $12,072.00\\\)

Adding up the future values:

\(Total FV = FV_1 + FV_2 + FV_3\)

= $20,296.43 + $15,618.04 + $12,072.00

≈ $47,986.47

Therefore, the future value of the fund on January 1, 2018, just after the third deposit, is approximately $47,986.47.

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Graph A. Correctly represents Macro's pay and work hours.

The equation of a line in slope-intercept form is y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

From the given graphs, B and C are definitely not the correct options as they are constant functions, and working for more hours would be earning more money.

Given, He earned $2560 for working 80 hours.

Therefore, In 8 hours he must have earned $256.

Graph A is the correct choice because at 8 hours earned money is approximately $260.

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Answer:

small triangle area = 1/2(8)(14) = 56 m²

bigger triangle area = 1/2(16)(14) = 112 m²

biggest triangle area = 1/2(24)(14) = 168 m²

there's 2 bigger triangles so you pick the bigger one you want

Answer:

smaller triangle area = 56m²

larger triangle area = 112m²

total area = 168m²

Step-by-step explanation:

Area of triangle = \(\frac{bh}{2}\)

where b = base length and h = height

smaller triangle dimensions

base length= 8m

height = 14m

* plug in the values into the formula *

\(area=\frac{8*14}{2} \\8*14 =112\\\frac{112}{2}=56\\A=56m^2\)

so we can conclude that the area of the smaller triangle is 56 square meters

larger triangle dimensions

base length = 16m

height = 14m

* plug in the values into the formula *

\(area=\frac{16*14}{2} \\16*14=224\\\frac{224}{2} =112\\A=112m^2\)

so we can conclude that the area of the larger triangle is 112 square meters

total area = the sum of the two triangle's area

total area = 112 + 56

112 + 56 = 168

hence the total area is 168 square meters

Answer:

367/90

Step-by-step explanation:

As \(4.\bar{7}=4\frac{7}{9}\), this means that \(0.4\bar{7}=4\frac{7}{90}=\frac{367}{90}\), 1/10th of 4.7 repeated.

The volume of the table tent 3 cmH8 cm12 cm is 288 cubic cm.

The volume of the table tent can be found by multiplying the length, width, and height of the tent.

Volume = length x width x height

In this case, the length is 12 cm, the width is 8 cm, and the height is 3 cm.

Volume = 12 cm x 8 cm x 3 cm

Volume = 288 cubic cm

Therefore, the volume of the table tent is 288 cubic cm.

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Answer:

angleWTR + angleWTU = 180°

Thus they are supplementary.

Option B.

Answer:

(x + 8)(x + 3)

Step-by-step explanation:

Given

x² + 11x + 24

Consider the factors of the constant term (+ 24) which sum to give the coefficient of the x- term (+ 11)

The factors are + 8 and + 3 , since

8 × 3 = + 24 and 8 + 3 = + 11 , then

x² + 11x + 24 = (x + 8)(x + 3) ← in factored form

Answer:

All three products were already rounded to the nearest 5g.

"Algebra made Easy" 450g

“Terrible Trigonometry" 95g

Wrapping 120g

867.107844 Is the maximum Jemima might have to pay to post the parcel.

Step-by-step explanation:

510 divided by 79 = 6.455g per 510g

665g total of products so divide 665 by 510 now to get 1.30392157g per weight which brings us to the maximum total of 867.107844

(150^3) Divided by 600 equals 5,625.

The (150^3) divided by 600, the value of 150 raised to the power of 3.

150^3 means multiplying 150 by itself three times.

150^3 = 150 * 150 * 150

Calculating the multiplication:

150 * 150 = 22,500

22,500 * 150 = 3,375,000

So, 150 raised to the power of 3 is equal to 3,375,000.

Now, we can divide 3,375,000 by 600 to find the final result.

3,375,000 / 600 = 5,625

Therefore, (150^3) divided by 600 equals 5,625.

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Answer:

B. 11

Step-by-step explanation:

We can try it for each

10*2+5=25

25-10=15❌

11*2+5=27

27-11=16 ✔

12*2+5=29

29-12=17❌

6*2+5=17

16-6=11❌

So it's B

The domain of the function giving the total time she swims according to the number of laps is:

10 ≤ laps ≤ 20.

The domain and the range can be explained by these two following bullet points:

In the context of this problem, the total time she swims is calculated according to the number of laps that she swims, hence the input and the output are defined as follows:

As stated in the problem, every day she swims between 10 and 20 laps, inclusive, hence the domain of the relation is given as follows:

10 ≤ laps ≤ 20.

The problem asks for the domain of the relation.

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The uncertain digit in the measurement 127.4 mL is the last digit, which is 4.

In the given measurement of 127.4 mL, the implied uncertainty can be determined by considering the precision of the measurement.

The presence of one decimal place, after the digit 4, suggests that the measurement has a precision of 0.1 mL.

This means that the measurement is accurate to the nearest tenth of a milliliter.

The uncertain digit is the digit that represents the estimated or uncertain value. In this case, the uncertain digit is the last digit, which is 4.

It signifies that there is some level of uncertainty in the exact value of the measurement and that it could vary by ±0.1 mL.

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Answer:

R: {y | -11 ≤ y < 11}

Step-by-step explanation:

Range is going to include the possible output values in regards to the Y-axis on the graph. As far as when to use equal to and not, the open circle means it does NOT include that number, since the circle is not colored in on that number, while the full circle DOES include that number, and that is when you would introduce the equal than.

Hope this helps.

Answer:

diameter = 36 in.

Step-by-step explanation:

V = 4π r^3/3

24416.64 = (4(3.14) r^3)/3

73249.92 = 12.56 r^3

r^3 = 5832

r = cube root of 5832 = 18

diameter = 36 in.

Answer:

434083

Step-by-step explanation:

\((1.12)^{20} * 45000 = 434083\)

Answer:

about 0.075

Step-by-step explanation:

The estimation of the quotient 1.64 divided by 22 is 0.0745.

Given that,

Based on the above information, the calculation is as follows:

\(= 1.644 \div 22\)

= 0.0745

Therefore we can conclude that the estimation of the quotient 1.64 divided by 22 is 0.0745.

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Answer:

144 miles

Step-by-step explanation:

Answer: (-1.5,0), (-6,9), (3, -9)

Step-by-step explanation:

The percentage of players weighing less than or equal to 233 pounds is 88.04%.

Percentage

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

See attachment for box plot,

From the box plot, the maximum is ,

Max = 244

the maximum is.

Min = 152

Percentage less than 233 is calculated as:

percentage = (233 - min)/ max - min

percentage = (233 - 152)/ 244 - 152

percentage = 81/92

express as percentage,

= 81/92 *100

= 8100/92

= 88.04%

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Answer: 75%

Step-by-step explanation: got it right

Answer:

m=3n

Step-by-step explanation:

3 movies per month. So 3 n per m.

Answer:

n=3m

Step-by-step explanation:

n is number of movies

3 is the 3 movies per month

m is each month

so it's n=3m