Suppose that Mars rotates on its axis once every hours. The equator lies on a circle with a diameter of miles.
(a) Find the angular speed of a point on its equator in radians per day ( hours).
(b) Find the linear speed of a point on the equator in miles per day.

Do not round any intermediate computations, and round your answer to the nearest whole number.

The probability that a point falls in the red-shaded square is given as follows:

p = 9/16.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The probability that a point falls in the red shared square is then given by the division of the area of the red shaded square by the division of the area of the larger square.

The area of the red-shaded square is given as follows:

3² = 9.

The area of the larger square is given as follows:

4² = 16.

Hence the probability is given as follows:

p = 9/16.

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Answer:

The answer is

\(y = \frac{4}{3} x + \frac{2}{3} \\ \)

Step-by-step explanation:

To find an equation of a line when given the slope and a point we use the formula

\(y - y_1 = m(x - x_1)\)

where

m is the slope

( x1 , y1) is the point

From the question the point is (-5,-6) and the slope is 4/3

The equation of the line is

\(y + 6 = \frac{4}{3} (x + 5) \\ y + 6 = \frac{4}{3} x + \frac{20}{3} \\ y = \frac{4}{3} x + \frac{20}{3} - 6\)

We have the final answer as

\(y = \frac{4}{3} x + \frac{2}{3} \\ \)

Hope this helps you

Answer:

∠s = 158

Step-by-step explanation:

Since lines a and b are parallel,

∠s and 158 are alternate exterior angles.

Alternate exterior angles are equal if two lines are parallel.

So,

∠s = 158

Answer: 22°.

Step-by-step explanation: We're given the angle 158°, which is all we need. Angle u and 158°, have to add up to 180°.  180° - 158° = 22°, which is the angle measure of u.  You're probably wondering how this will help us.  The answer to that is it gives us the measurement of angle t, which is 158°.  Now, we'll do the same thing we did with angle u, which was to make angle u add up with 158° to make 180°.  We'll apply this to angle t and angle s.  We already know that angle t is 158°, so angle s has to be 22° in order to add up to 180°.  Therefore, your answer is 22° for angle s.

Let me know if this is right! :)

Base on the total area of the square garden and the number of plants planted on it, the area of the zucchini section is 15 feet²

Side Length of the square garden = 8 feet

Area of the garden = side length ²

= 8 feet × 8 feet

= 64 feet²

Flower portion:

Side Length = 2 feet

Area of flower portion = side length ²

= 2 feet × 2 feet

= 4 feet²

Remaining space = Area of the garden - Area of flower portion

= 64 feet² - 4 feet²

= 60 feet²

Remaining space is divided into 4 equal sections

= 60 feet² / 4

= 15 feet²

Therefore,

Tomatoes section = 15 feet²

Onions section = 15 feet²

Zucchini section = 15 feet²

Pepper section = 15 feet²

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Step-by-step explanation:

The expression you provided involves taking the square root of a negative number, which results in an imaginary number. In standard real number arithmetic, the square root of a negative number is undefined. However, in the realm of complex numbers, we can define a square root of negative numbers using the imaginary unit "i," where i is defined as the square root of -1.

Let's break down the expression step by step:

√(-25) / √9

The square root of -25 can be written as √(-1 * 25), which can further be simplified as √(-1) * √25.

√(-1) is equal to "i," and the square root of 25 is 5.

So, the expression becomes:

i * 5 / √9

The square root of 9 is 3.

Now, we can simplify further:

i * 5 / 3

Thus, the simplified expression is (5i) / 3, where "i" represents the imaginary unit.

Answer:

the answer is 30.75 or 30 1/4

Step-by-step explanation:

8 can't go into 2 so 8 will go into 24

8 can go into 24 3 times thats our first digit

then multiply 8 times 3 you will get 24 write that under 24

then subtract 24 from the original 24 you will get 0

bring down the 6 to where the 0 is try to divide 8 into three

because you can't u will add a 0 next to the three

that is how you get the 30

thats as much as I know sorry I used the calculator

Answer:  He will weigh 112 lbs at 1000 miles up

Answer:

2√2 units.

Step-by-step explanation:

To find the length of the line joining points A(3, 5) and B(1, 3), we can use the distance formula. The distance formula is given by:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the coordinates of points A and B into the formula, we have:

d = sqrt((1 - 3)^2 + (3 - 5)^2)

  = sqrt((-2)^2 + (-2)^2)

  = sqrt(4 + 4)

  = sqrt(8)

  = 2sqrt(2)

Therefore, the length of the line joining points A and B is 2√2 units.

Answer:

WN=37.8

Step-by-step explanation:

WN=18%*210

WN=0.18*210

WN=37.8

pi * d/2 + 5*2+7

It is a half circle

10.99+10+7

27.99

In year 2056 the population of the region reach 12, 000,000.

The natural logarithm, also known as the logarithm to base e, is a logarithm function that uses the number e (approximately 2.718) as its base. The natural logarithm of a number x is denoted as ln(x) or log e (x). It is the inverse function of the exponential function with base e.

The natural logarithm has several properties that make it useful in mathematics and science. For example, it can be used to solve equations that involve exponentials, and it can also be used to simplify certain types of equations in calculus.

One of the most important properties of natural logarithm is log(ab)=log(a)+log(b) which is known as logarithm property.

In addition to its mathematical uses, the natural logarithm also appears in many areas of science, such as in physics and engineering, where it is used to model natural phenomena that involve exponential growth or decay.

The annual growth rate of Bicol Region is 1.02%, which means that the population of the region is increasing by 1.02% every year. To find the year when the population of the region will reach 12,000,000, we can use the formula for population growth:

P = P0(1 + r)^n

Where P is the final population, P0 is the initial population, r is the growth rate, and n is the number of years.

So, we know that:

P = 12,000,000

P0 = 6,000,000

r = 0.0102 (convert the growth rate to decimal form)

Now we can plug these values into the equation and solve for n:

12,000,000 = 6,000,000(1 + 0.0102)^n

We can simplify this equation by taking the natural logarithm of both sides:

ln(12,000,000) = ln(\(6,000,000(1 + 0.0102)^{n}\))

ln(12,000,000) = ln(6,000,000) + nln(1 + 0.0102)

We can then isolate n by subtracting ln(6,000,000) from both sides:

nln(1 + 0.0102) = ln(12,000,000) - ln(6,000,000)

n = (ln(12,000,000) - \(\frac{ln(6,000,000))}{ln(1 + 0.0102)}\)

Rounded to the nearest year, the population of the Bicol Region will reach 12,000,000 in year 2056

Please note that the model is assuming that the growth rate is only affected by natural increase and migration, and there's no external factors that could change the population of the region.

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Answer:

50

Step-by-step explanation:

parentheses...2×3=6...6+10=16

30-16+4+32

50

Answer: 8 books

Step-by-step explanation:

y= how much shelf space take up (inches)

x= # of books

y=2x

in this situation 16=y

16=2x

divide both sides by 2

8=x

Answer:step 2

Step-by-step explanation:

It is better to apply the 10% off coupon first and then the $2 off coupon.

Let's assume the price of the pizza is P.

If we apply the $2 off coupon first, the price of the pizza would be reduced to $P-2$. Then, if we apply the 10% off coupon, the price would be further reduced by 0.1(P-2). Therefore, the total price paid would be:

\($$P_{total}=P-2-0.1(P-2)=0.9P-1.8$$\)

If we apply the 10% off coupon first, the price of the pizza would be reduced to 0.9P. Then, if we apply the $2 off coupon, the price would be further reduced by 2. Therefore, the total price paid would be:

\($$P_{total}=0.9P-2$$\)

Comparing the two total prices, we can see that:

\($$0.9P-1.8 < 0.9P-2$$\)

Therefore, it is better to apply the 10% off coupon first and then the $2 off coupon.

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The area of the ring formed by concentric circles is approximately 188.5 square units.

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

The ring is formed by two concentric circles.

The area of the ring can be found by subtracting the area of the smaller circle from the area of the larger circle.

The area of a circle with radius r is given by the formula A = πr².

So, the area of the larger circle with radius 16 is -

A1 = π(16)² = 256π

And the area of the smaller circle with radius 14 is -

A2 = π(14)² = 196π

Therefore, the area of the ring is -

A ring = A1 - A2

A ring = 256π - 196π

A ring = 60π

To round to the nearest tenth, we can approximate π as 3.14 -

A ring ≈ 60 × 3.14 = 188.4

Rounding to the nearest tenth, we get -

A ring ≈ 188.4 ≈ 188.5

Therefore, the area of the ring is 188.5 square units.

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Answer:

Fred spent $3.18 on brownies.

Answer:

f(5) = 21, f(-2) = 0

Step-by-step explanation:

f(5) = 3(5 + 2) = 3(7) = 21

f(-2) = 3(-2 + 2) = 3(0) = 0

Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.

Algebra is the branch of mathematics that deals with numbers and values which are represented with letters and symbols.

Sometimes, we do not want to mention a particular number, we can represent the number by a letter or a suitable symbol. This approach is algebraic.

For example, d + d = 2d

This is an example of an algebraic expressionns.

Given the algebraic expressions,

\(\frac{1}{2}x + 4 \\ x + 6 - \frac{1}{2}x - 2\)

Substituting 2 for x in the first expression gives:

(1/2 × 2) + 4

1 + 4

5

Substituting 2 for x in the second expression gives:

2 + 6 - (1/2 ×2) - 2

8 - 1 - 2

8 - 3

5

Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.

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Answer:

the first one is (23)

number 7 is ( 34.069)

Step-by-step explanation:

Answer:

420.99 -> four-hundred twenty and ninety-nine hundreths

Step-by-step explanation:

All above

Answer:

(3,-10) try plotting all points and you'll find your answer.

A digit to make the number divisible by 3 is by adding the digit 2 to the number 1234.

To make the number 1234 divisible by 3, we can find the sum of its digits and determine if it is divisible by 3. If the sum of the digits is divisible by 3, then the original number is also divisible by 3.

Let's calculate the sum of the digits in 1234:

1 + 2 + 3 + 4 = 10

The sum of the digits is 10. Since 10 is not divisible by 3, we need to add or subtract a digit to make the sum divisible by 3.

To find the digit we need to add or subtract, we can use the fact that the difference between the original sum and the next multiple of 3 is the required digit.

The next multiple of 3 greater than 10 is 12 (12 - 10 = 2). Therefore, we need to add 2 to the number 1234 to make it divisible by 3.

1234 + 2 = 1236

we obtain the number 1236, which is divisible by 3.

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The sοlutiοns tο the quadratic equatiοn \(x^2 - 11x - 60 = 0\) are x = 15 and x = -4.

Each quadratic prοblem can be sοlved using the quadratic fοrmula. The equatiοn is first changed tο have the fοrm \(ax^2+bx+c=0\), where a, b, and c are cοefficients.

Tο sοlve fοr x in the quadratic equatiοn x² - 11x - 60 = 0, we can use the quadratic fοrmula:

\(x = (-b \± \sqrt{(b^2 - 4ac))} / 2a\)

where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.

In this case, a = 1, b = -11, and c = -60. Substituting these values into the quadratic formula, we get:

\(x = (-(-11) \± \sqrt{((-11)^2 - 4(1)(-60)))} / 2(1)\)

Simplifying the expression under the square root, we get:

\(x = (11 \± \sqrt{(121 \+ 240))} / 2\\x = (11 \± \sqrt{(361)) / 2}\\x = (11 \± 19) / 2\)

So we have two solutions:

x = (11 + 19) / 2 = 15

x = (11 - 19) / 2 = -4

Therefore, the solutions to the quadratic equation x² - 11x - 60 = 0 are x = 15 and x = -4.

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Answer:

  half

Step-by-step explanation:

Dividing a number by 2 is the same as multiplying it by 1/2. We can say the result is half the number's value.

Steve is correct. Steve can find the difference in temperature between 7 AM and 12 PM on Wednesday by adding the distances from 0.

By using a number line, Steve can find the difference in temperature between 7 AM and 12 PM on Wednesday by adding the distances from 0. One temperature is negative and the other is positive, but by adding their distances, he can find the difference. Kelly's method of subtracting -5.1 from the temperature at 12 PM on Wednesday is not necessarily incorrect, but it does not give the exact difference in temperature between the two times. Therefore, using Steve's method, the change in temperature would be the sum of the distance from 0 to the temperature at 7 AM (which is 2.5) and the distance from 0 to the temperature at 12 PM (which is also 2.5), resulting in a difference of 5 degrees.

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