8. Gavin goes to the market and buys one rectangle shaped board. The
length of the board is 16 cm and width of board is 10 cm. If he wants to add
a 2 cm wooden border around the board, what will be the area of the
rectangle board?

The number of square feet needed to cover the hole is 44ft²

To find this, we need to find the area of the green region and subtract the little square that it has inside.

Remember that for a rectangle, the area is the product between the dimensions, then the area of the green region is:

A = 12ft*4ft = 48ft²

The little square has an area:

a = 2ft*2ft = 4ft²

Then the area needed is:

area = 48ft² - 4ft² = 44ft²

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Answer:

i just kno that D is 0

Step-by-step explanation:

-7 +7=0

Answer:

Given:

Area of the sector (A) = 104π/9 square inches

Central angle (θ) = 65 degrees

The formula for the area of a sector of a circle is:

A = (θ/360) * π * r^2

We can rearrange this formula to solve for the radius (r):

r^2 = (A * 360) / (θ * π)

Plugging in the given values:

r^2 = (104π/9 * 360) / (65 * π)

r^2 = (104 * 40) / 9

r^2 = 4160 / 9

r^2 ≈ 462.22

Taking the square root of both sides:

r ≈ √462.22

r ≈ 21.49

Therefore, the radius of the circle is approximately 21.49 inches.

Answer: 8 inches

Step-by-step explanation:

The  distance hiked by Keenan in terms of m is \(\frac{15m}{16}\)

The given parameters;

Let the distance Margot hiked = n

Then, the distance keenan hiked = 15n

The total distance hiked by both: m = n + 15n

The distance hiked by Margot in terms of m is calculated as;

m = n + 15n

m = 16n

\(n = \frac{m}{16}\)

The distance hiked by Keenan in terms of m is calculated as;

=  15(n)

\(= 15(\frac{m}{16} )\\\\= \frac{15 m}{16}\)

Thus, the  distance hiked by Keenan in terms of m is \(\frac{15m}{16}\)

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Answer:

See below

Step-by-step explanation:

Starting with 42, there would be two branches of 2 and 21 connected to 42. Since 2 is prime, there are no more branches. Since 21 is composite, then two more branches are drawn of 3 and 7 connected to 21. Since 3 and 7 are prime, there are no more branches.

Therefore, the prime factorization of 42 is 2*3*7, and its factors would be 1,2,3,6,7,14,21,42.

A. P(6, then 1) = 1/90

B. P(even, then 5) = 1/18

C. P(8, then odd) = 1/18

D. P(3, then prime) = 2/45

E. P(prime, composite) = 4/15

F. P(even, then 3, then 5) = 1/144

Given:

Total number of cards: 10

A. P(6, then 1):

P(6, then 1) = 1/10 x 1/9

= 1/90

B. P(even, then 5):

Number of favorable outcomes: 5 x 1 = 5

P(even, then 5) = 5/10 x 1/9

= 1/18

C. P(8, then odd):

Number of favorable outcomes: 1 x 5 = 5

P(8, then odd) = 1/10 x 5/9

= 1/18

D. P(3, then prime):

Number of favorable outcomes: 1 x 4 = 4

P(3, then prime) = 1/10 x 4/9

= 2/45

E. P(prime, composite):

Number of favorable outcomes: 4 x 6 = 24

P(prime, composite) = 4/10 x 6/9

= 4/15

F. P(even, then 3, then 5):

Number of favorable outcomes: 5 x 1 x 1 = 5

P(even, then 3, then 5) = 5/10 x 1/9 x 1/8

= 1/144

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A situation in which positive and negative numbers are used to describe values that have opposite meaning is that John is on top of a mountain that is 2000 above sea level and his friend is diving and is below 2000 feet.

The thing that 0 represents is the addition in the sea level.

Based on the information illustrated, the situation will be that John is on top of a mountain that is 2000 above sea level and his friend is diving and is below 2000 feet.

Therefore, the addition will be:

= 2000 + (-2000)

= 2000 - 2000

= 0

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Answer:

Yes

Step-by-step explanation:

I'm pretty sure that 4 is leaning towards the opposite of b

Answer: 60.004

Step-by-step explanation:

56 x 0.0715= 4.004

56+4.004= 60.004

It will take 150 minutes for the two containers to have the same amount of water.

To find the number of minutes it will take for the two containers to have the same amount of water, we need to use the following formula:

m = |A - B| / (a - b)

where m is the number of minutes, A is the initial amount of water in Container A, B is the initial amount of water in Container B, a is the rate at which water is being added to Container A, and b is the rate at which water is being drained from Container B.

In this case, the initial amount of water in Container A is 300 liters, the initial amount of water in Container B is 900 liters, the rate at which water is being added to Container A is 6 liters per minute, and the rate at which water is being drained from Container B is 2 liters per minute. Substituting these values into the formula, we get:

m = |300 - 900| / (6 - 2)

m = |-600| / 4

m = 600 / 4

m = 150 minutes

Therefore, it will take 150 minutes for the two containers to have the same amount of water.

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Answer: D

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

brainliest:)

Solution:

Step-1: Find the area of the rectangle.

L = 5/8 foot; B = 4/9 foot

Step-2: Verify all the options.

Looking at all the options, we can see that Option C (1/4 ft²) is the best estimate of the area we obtained as 10/36 and 9/36 are really close fractions.

Thus, Option C is correct.

When 1,493,600 is divided by 8 the quotient is 186,700.

To divide 1,493,600 by 8, you can follow these steps:

We have to write down the dividend (1,493,600) and the divisor (8).

Now start with the largest place value in the dividend (the leftmost digit) and perform the division.

Divide 1 by 8. Since 1 is smaller than 8, you move to the next digit.

Bring down the next digit (4) and combine it with the previous quotient (0). This gives you 04.

Divide 4 by 8. Since 4 is smaller than 8, you move to the next digit.

Bring down the next digit (9) and combine it with the previous quotient (0). This gives you 09.

Divide 9 by 8. The quotient is 1, and the remainder is 1.

Bring down the next digit (3) and combine it with the remainder (1). This gives you 13.

Divide 13 by 8. The quotient is 1, and the remainder is 5.

Bring down the next digit (6) and combine it with the remainder (5). This gives you 56.

Divide 56 by 8. The quotient is 7, and there is no remainder.

Bring down the next digit (0) and combine it with the quotient (7). This gives you 70.

Divide 70 by 8. The quotient is 8, and there is no remainder.

There are no more digits to bring down, and the division is complete.

The quotient is the result of the division. In this case, 1,493,600 divided by 8 is equal to 186,700.

Therefore, the result of 1,493,600 ÷ 8 is 186,700.

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The rectangular coordinates of the polar coordinates (3√5, -π/8) are approximately (3.35, -0.77).

To convert polar coordinates (r, θ) to rectangular coordinates (x, y), we use the following formulas:

x = r * cos(θ)

y = r * sin(θ)

In this case, the given polar coordinates are (3√5, -π/8).

Applying the formulas, we have:

x = (3√5) * cos(-π/8)

y = (3√5) * sin(-π/8)

Evaluating the trigonometric functions using a calculator or trigonometric tables, we find:

x ≈ 3.35

y ≈ -0.77

Rounding these values to the nearest hundredth, the rectangular coordinates of the polar coordinates (3√5, -π/8) are approximately (3.35, -0.77).

Please note that the angle -π/8 represents a counterclockwise rotation of π/8 radians from the positive x-axis in the Cartesian coordinate system.

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The statement which best describes Gary’s error is; Gary did not use the greatest common factor in the equation.

This is the largest positive integer or polynomial that is a divisor of several different numbers. For instance, the greatest common divisor of 66, 30 and 18 is 6.

Gary's work:

66 + 36

Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66

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

66 + 36

= 3 (22 + 12)

Gary did not use the greatest common factor in the equation.

The correct answer:

66 + 36

= 6(11 + 6)

Therefore, Gary did not use the greatest common factor in the equation.

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Answer:

1. wire is approx. 143.96 ft

2. pole is approx. 106.55 ft

Step-by-step explanation:

Mapping the information on the SOHCAHTOA picture below:

Φ = 46

wire = hypotenuse

adjacent side = 100

CAH is most suitable:

cos 46° = 100/wire => wire = 100/cos 46 ≈ 143.96

pole = opposite side + 3

TOA is most suitable:

tan 46° = (pole-3)/100 => pole = 3 + 100 * tan 46 ≈ 106.55

By using some exponent properties, we can simplify the expression to get:

√(100)² = 100

Here we will be using two exponent properties, these are:

√a = a^(1/2)

And:

(a^n)^m = a^{n*m}

The given expression here is:

√(100)²

Using the first property, we can rewrite this as:

( 100¹/²)²

And using the second property, we can rewrite as:

( 100¹/²)² = 100²*⁽¹/²⁾ = 100¹ = 100

That is the simplified expression.

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Answer:

y = 1 , x = - 1

Step-by-step explanation:

2x - 3y = - 5 → (1)

y = 2 + x ( subtract 2 from both sides )

y - 2 = x or x = y - 2

substitute x = y - 2 into (1)

2(y - 2) - 3y = - 5

2y - 4 - 3y = - 5

- y - 4 = - 5 ( add 4 to both sides )

- y = - 1 ( multiply both sides by - 1 )

y = 1

---------------------------------------------

substitute y = 1 into y = 2 + x

1 = 2 + x ( subtract 2 from both sides )

- 1 = x

Answer: he will be 14

Step-by-step explanation:

Anna is 14 and her brother is 10. Two years ago she was 12. 3/4 of 12 is 9. 9+5 more years is 14. :)))

Answer:

z = 99

Step-by-step explanation:

\(\frac{z}{9}\) + 4 = 15 ( subtract 4 from both sides )

\(\frac{z}{9}\) = 11 ( multiply both sides by 9 to clear the fraction )

z = 99

Differentiate both sides with respect to \(t\), treating both \(x\) and \(y\) as functions of \(t\).

\(x^3 + y^3 = 9 \implies 3x^2 \dfrac{dx}{dt} + 3y^2 \dfrac{dy}{dt} = 0\)

Then when \(x=1\), \(y=2\) and \(\frac{dx}{dt}=-3\), we get

\(3\times1^2\times(-3) + 3\times2^2\dfrac{dy}{dt} = 0 \implies \dfrac{dy}{dt} = \dfrac9{12} = \boxed{\frac34}\)

Answer:

3 6 8

Step-by-step explanation:

i just need them points.

Answer:

−200y − 2

Step-by-step explanation:

y(2.5 + 7) + y −210.5y − 2

=9.5y + y + −210.5y + −2

=(9.5y+ y + −210.5y) + (−2)

−200y − 2

Mark me brainllest

The total cost equation can be written as:

Total Cost = 32000 + 9000L

What is total cost?

Total cost refers to the complete amount of money or resources that are required to produce or obtain a particular good or service. It includes all of the expenses associated with production, such as labor costs, materials costs, overhead costs, and any other costs necessary to manufacture or acquire the product.

The total cost equation can be expressed as:

Total Cost = Fixed Cost + Variable Cost

where Fixed Cost is the cost that does not vary with the number of laptops manufactured and sold, and Variable Cost is the cost that depends on the number of laptops manufactured and sold.

In this case, the fixed monthly cost is $32,000 and it does not depend on the number of laptops manufactured and sold. The variable cost is the cost of manufacturing each laptop, which is $9,000 per laptop.

If L is the number of laptops manufactured and sold per month, then the variable cost can be expressed as 9000L. Therefore, the total cost equation can be written as:

Total Cost = 32000 + 9000L

This equation represents the total cost of manufacturing and selling L laptops per month. The fixed cost of $32,000 is added to the variable cost of $9,000 per laptop multiplied by the number of laptops sold, L, to obtain the total cost.

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Complete question: A business manufactures and sell laptops. Each laptop is sold for 14000.the fixed monthly cost is 32000 and it cost 9000 to manufacture each laptop. let L be number of laptops manufactured and sold per monthly. What is the total cost equation?

Answer:

There were 24 females and 36 men on the bus

Step-by-step explanation:

To find the amount of females on the bus you multiply the 60 passengers by 0.4 to mimic the 40% and you get 24. So there were 24 females and to find the men you simply subtract 24 and 60 to get 36

Answer: A, C

Step-by-step explanation:

Diagonals of a parallelogram bisect each other, so \(4x-7=2x+1 \longrightarrow x=4\). So \(ED=4(4)-7=\boxed{9}\).

Opposite sides of a parallelogram are congruent, so \(8y-3=3y+7 \longrightarrow y=2\), so \(AD=8(2)-3=\boxed{13}\)

Answer: 112.5 hours

Step-by-step explanation:

y < -3.

\(5(-3) > 7y +6\)

\(-15 > 7y +6\)

\(-15-6 > 7y +6-6\\ \\-21 > 7y\)

\(\frac{-21}{7} > \frac{7y}{7} \\ \\-3 > y\\ \\y < -3\)

In order to verify the answer, we must take the calculated value of "y" and substitute it by "y" in the original expression. The final result should be the inequality showing the same value on both sides of the symbol.

\(5(-3) > 7(-3) +6\\ \\-15 > -21+6\\ \\-15 > -15\)

That's correct! Hence, y < -3 is the correct answer.