write down the rational number
whose numerator = 8 , denominator = 9​

The top of the 17-foot ladder is sliding down the wall at a rate of -16/7.5 feet per second (negative sign indicates downward direction) when the bottom is 8 feet from the wall.

To find how fast the top of a 17-foot ladder is sliding down the wall when the bottom is 8 feet from the wall, given that the bottom slides away at a constant rate of 4 feet per second.

First, let's set up the problem using the given information. Let x represent the distance from the bottom of the ladder to the wall, and y represent the distance from the top of the ladder to the ground. According to the Pythagorean theorem, we have:

\(x^2 + y^2 = L^2\), where L is the length of the ladder, 17 feet in this case.

Now, we are given that the bottom of the ladder, x, is sliding away from the wall at a constant rate of 4 feet per second, so dx/dt = 4 ft/s.

Our goal is to find dy/dt, the rate at which the top of the ladder is sliding down the wall, when x = 8 feet.

First, differentiate both sides of the Pythagorean equation with respect to time t:

2x(dx/dt) + 2y(dy/dt) = 0

When x = 8 feet, we can find y by plugging the value into the Pythagorean equation:

\(8^2 + y^2 = 17^2\)
\(y^2 = 289 - 64\)
\(y^2 = 225\)
y = 15

Now, plug the values x = 8, y = 15, and dx/dt = 4 into the differentiated equation:

2(8)(4) + 2(15)(dy/dt) = 0

Simplify and solve for dy/dt:

64 + 30(dy/dt) = 0
dy/dt = -64 / 30
dy/dt = -16 / 7.5

Therefore, the top of the 17-foot ladder is sliding down the wall at a rate of -16/7.5 feet per second (negative sign indicates downward direction) when the bottom is 8 feet from the wall.

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Answer:

I attached both the work and explanation down below. Hope it helps!

Answer:

Your answer is 8/3 or 2 2/3.

Step-by-step explanation:

4/5 * 10/3

Hope this helps!

Leo could buy 1.5 pounds of strawberries if they cost $2.80 per pound.

From the question, we have the following parameters that can be used in our computation:

3. 5lbs of strawberries that cost $4.20.

This means that

Cost = $4.20

Pounds = 3.5

For a unit rate of 2.8 we have

Pounds = 4.20/2.8

Evaluate

Pounds = 1.5

Hence, Leo could buy 1.5 pounds of strawberries if they cost $2.80 per pound.

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Let's begin by finding the mean of the data

Mean = 48.9

Next, we calculate the absolute value of the difference between each data value and the mean, we have:

|data value – mean|

|46 - 48.9| = 2.9

|47 - 48.9| = 1.9

|56 - 48.9| = 7.1

|48 - 48.9| = 0.9

|46 - 48.9| = 2.9

|52 - 48.9| = 3.1

|57 - 48.9| = 8.1

|52 - 48.9| = 3.1

|45 - 48.9| = 3.9

Next, we sum up the absolute values of the differences (from above) & divide by the number of data values, we have:

MOD = 8 (to the nearest whole number)

Answer:

5/16=s/32

Step-by-step explanation:

What we know:

- a school team has 80 swimmers

The ratio of 7th grade swimmers to every swimmer in their school (counting all the grades) is 5:16. Write a proportion of this for a value of s.

a ratio can also be expressed in a fraction by simply putting it from x:y to x/y

so, the ratio 5:16 can also be expressed as 5/16.

note: let sgs represent seventh grade swimmers.

also, let x represent the value of the equivalent amount of swimmers (in the denominator that serves as a value for the proportion of 5/16.

we need to find:

5 sgs/16 swimmers = s amount of sgs/x

5/16=s/x

equivalent fractions could literally be anything, just multiply that ratio by a value equal to one; ex 4/4, or 16/16, or 2/2.

the simplest proportion is to multiply 5/16 by 2/2.

5/16*(2/2)=s/x

10/32=s/x

so s=10 and x=32 but we only need to know x cuz your problem doesn't have a box to answer the s=10.

so... 5/16=s/32.

A regular octahedron has 6 vertices that are equally spaced on the surface of a sphere. Any plane passing through three or more of these vertices will intersect the sphere in a circle. We can count the number of planes by counting the number of circles formed.

Each of the 8 faces of the octahedron is an equilateral triangle with 3 vertices. Therefore, each face contributes ${3\choose 3}=1$ circle, and there are a total of 8 circles.

In addition, there are 6 diagonals of the octahedron connecting opposite vertices. Each diagonal passes through the center of the sphere and intersects the sphere in two points, dividing the sphere into two hemispheres. Any plane containing one of these diagonals will intersect each hemisphere in a circle, for a total of 12 circles.

Therefore, the total number of planes passing through three or more vertices of a regular octahedron is 8+12=20.

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Complete Question

An octahedron is a regular solid with 6 vertices and 8 faces. How many planes pass through three or more vertices of a regular octahedron?

Answer:d. 6500

Step-by-step explanation:

Answer: D)$6500

Step-by-step explanation: took the quiz

(a)The levels of production that will yield a profit of $359,400 are approximately 292.36 and 651.64 units. (b)So, it is possible to make a profit of more than $359,400.

(a) To determine the level(s) of production that will yield a profit of $359,400, substitute P=359400 in the equation.6400x−18x^2−400 = 359400Adding 400 to both sides:6400x − 18x² = 359800

Dividing both sides by -2:9x² − 3200x + 179700 = 0

Applying the quadratic formula:

x = (-(-3200) ± √((-3200)² - 4(9)(179700))))/(2(9))

= (3200 ± √(10240000 - 6464400))/18

= (3200 ± √(3785600))/18

= (3200 ± 1946.55)/18x

= 292.36 or 651.64

Thus, the levels of production that will yield a profit of $359,400 are approximately 292.36 and 651.64 units.

(b) To determine if a profit of more than $359,400 can be made, we need to determine the maximum profit by completing the square, and comparing it to $359,400.P=6400x−18x^2−400

Completing the square: P= -18(x - 88.89)² + 710937.2

Maximum profit is $710,937.20, which is more than $359,400.

So, it is possible to make a profit of more than $359,400.

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Answer:

6,4 pounds

Step-by-step explanation:

First, let's the given numbers into improper fractions:

\(1 \frac{2}{3} = \frac{1 \times 3 + 2}{3} = \frac{5}{3} \)

\(2 \frac{2}{5} = \frac{2 \times 5 + 2}{5} = \frac{12}{5} \)

Now, we can find how much does the 2nd bar weigh by multiplying the 1st bar's weight by 5/3 times:

\( \frac{5}{3} \times \frac{12}{5} = \frac{60}{15} = 4\)

Finally, let's add both bars' weights and we'll get the answer:

\( \frac{4}{1} + \frac{12}{5} = \frac{4 \times 5}{5} + \frac{12}{5} = \frac{20 + 12}{5} = \frac{32}{5} = 6.4\)

Answer:

The dog has 1357.5 square feet of running space.

Step-by-step explanation:

48 feet is the diameter of the circle in which the dog can run, minus 1/4 of the total circle (assuming the dog can not run through walls).

The formula of how to find the area of a circle is...

A =  π r²

A stands for area, pi(π) is 3.14, and r means radius.

Radius is half of the diameter, so the radius would be 24 feet. Let's plug those numbers into the formula:

A = π x 24²

A = π x 576

A = 1809.56 square feet

Now, we have to subtract 1/4 of 1810 (rounded up).

1810 times 0.75 = 1357.5 feet.

I hope this helps you! :-)

Answer:

24

Step-by-step explanation:

√64 ×∛27

√64=√8²=8

∛27 = √3³=3

8*3=24

It will take 5 months for Eduardo and Peta to weigh the same.

Eduardo weighs 120 pounds and is gaining 5 pounds each month, so after 1 month he will weigh 120 + 5 = 125 pounds.

After 2 months he will weigh 125 + 5 = 130 pounds.

This pattern continues, so after n months he will weigh 120 + 5n pounds.

Peta weighs 160 pounds and is losing 3 pounds each month, so after 1 month she will weigh 160 - 3 = 157 pounds.

After 2 months she will weigh 157 - 3 = 154 pounds.

This pattern continues, so after n months she will weigh 160 - 3n pounds.

We want to find the number of months it will take for Eduardo and Peta to weigh the same, so we set the expressions for their weights equal to each other and solve for n:

120 + 5n = 160 - 3n

8n = 40

n = 5

It will take 5 months for Eduardo and Peta to weigh the same.

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Answer:

u need to substitute (-8,5) in the equation because the line passses through that point

The area of the rectangular piece to be painted after cutting will be 1200 cm².

What is the definition of a rectangle?

Rectangles are four-sided polygons with 90-degree internal angles. Two sides meet at right angles at each corner or vertex. The rectangle is distinguished from the square by the fact that its opposite sides are of equal length.

If one side of a rectangle is 20 cm long, the opposite side is also 20 cm long.

A rectangle has two intersecting diagonals. The length of both diagonals is the same.

The perimeter is defined as P = 2 (Length + Width).

Area of a Rectangle=Length*Breadth

Now,

Length of cardboard=42cm

breadth=32 cm

Area of cardboard=42*32=1344cm²

Area of square to be cut=6*6=36cm²

and total 4 squares are cut

Then the area of the box that is made to be painted is =1344*4*36

=1200 cm²

hence,

          The area of the rectangular piece to be painted after cutting will be 1200 cm².

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Inequality stating that there are 8000 sq. m. of land available: Let B be the number of units of house B and C be the number of units of house C.

Therefore,B+C ≤ 8000/200 [Reason: House C requires 200 sq. m. of land]⇒B+C ≤ 40b. Inequality that the engineer has at most 6400 man-hour available for construction:

160B + 256C ≤ 6400c

Inequality stating that the engineer has at least 12 million pesos to spend for materials:

600B + 800C ≤ 12000d

. Let us write down a table to calculate the cost, income and profit as follows:Units of house BLabor Hours per unit of house BUnits of house CLabor Hours per unit of house CTotal Labor HoursMaterial Cost per unit of house BMaterial Cost per unit of house CTotal Material CostIncome per unit of house BIncome per unit of house C

Total IncomeTotal ProfitBC=8000/200-B160CB+256C600000800000+256C12,000,0003,500,0004,000,0003,500,000B+C ≤ 40 160B + 256C ≤ 6400 600B + 800C ≤ 12000 Units of house B requires 160 man-hour and a unit of house C requires 256 man-hour.

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Answer:

C

Step-by-step explanation:

find 2 on x axis

then fine 3 on Y axis

The equation of the line that represents the data in the table is y = 30x + 30.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept

From the data;

Point 1( 0,30 )

Point 2( 2,90 )

First, we determine the slope.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Slope m = ( 90 - 30 )/( 2 - 0 )

Slope m = ( 60 )/( 2 )

Slope m = 30

Next, we determine the y-intercept b by substituting the given values into the equation of line formula.

y = mx + b

30 = (30)0 + b

30 = b

b = 30

Now, plug these values into y = mx + b to determine the equation of the line.

y = mx + b

y = 30x + 30

Therefore, y = 30x + 30 is the equation of the line.

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Answer:

y=2

Step-by-step explanation:

Hey there!

The answer is y=2 because the x-axis is not defined (there's no value for it as the line didn't pass through it)

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

Parallel lines have the same slope.

So if the given line has a slope of 3, then the line parallel to it has the same slope (3)

Now, let's write the equation of the line in Point-Slope Form.

Remember, point-slope form looks like so:-

\(\bigstar{\underline{\boxed{\pmb{y-y1=m(x-x1)}}}\)

Where

y₁ is the y-coordinate of the point that the line passes through

m is the slope

x₁ is the x-coordinate of the point that the line passes through

In this case,

y₁ is equal to -8

m is equal to 3

x₁ is equal to 1

Plug in the values:

\(\longrightarrow\sf{y-(-8)=3(x-1)}\)

Simplify:

\(\longrightarrow\sf{y+8=3(x-1)}\)

and we're done!

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

Hope everything is clear; if you need any more explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)

Therefore , the solution of the given problem of unitary method comes out to be in a group of 15, we would anticipate that 5 pupils would choose a candy.

To finish a job using the unitary method, divide the lengths of just this minute subsection by two. In a nutshell, the unit method eliminates a desired item from both the characterized by a set and colour subsets. 40 pens, for instance, will cost Rupees ($1.01). It's conceivable that one nation will have complete control over the strategy used to achieve this. Almost all living things have a unique trait. There are changes and unanswered issues (mathematics, algebra).

Here,

There are a total of 12 sweets in the bag: 5 + 1 + 2 + 4 candies. Given that there are 4 gold-wrapped candies out of a total of 12, the chance of choosing one during any given draw is 4/12 = 1/3.

. Therefore, regardless of how many draws have been conducted before, the chance of choosing a gold-wrapped treat is always 1/3.

In a class of 15 pupils, the predicted proportion of students who would choose a gold-wrapped treat would be:

Expected number of gold-wrapped candies = (1/3) * (number of draws) * (probability of choosing gold-wrapped candy on one draw) = 5

Therefore, in a group of 15, we would anticipate that 5 pupils would choose a candy that was wrapped in gold.

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Answer

Your saviour has come!

The answer is A

Step-by-step explanation:

Answer:

i think point A ( -3 , 4)

(-3,4)

a) The sample space for four flights selected at random, with arrival status "O" for on-time and "L" for late, is given as {OOOO, OOOL, OOLO, OOLL, OLOO,  OLOL, OLLO, OLLL, LOOO, LOOL, LLOO, LLOL, LLLO, LLLL}.

b) The probability that a randomly selected flight is from Airline A and on-time, denoted as P(A), is calculated by multiplying the probability of being on-time for Airline A (75/100) with the proportion of flights operated by Airline A out of the total (320/1000), resulting in P(A) = 24/100.

c) The probability that a randomly selected flight is either from Airline C or on-time, denoted as P(C), is obtained by dividing the sum of flights on-time (700) and flights operated by Airline C (240) by the total number of flights (1000), giving P(C) = 94/100.

d) The probability that a flight is from Airline B given that it is late, denoted as P(B | L), is computed by multiplying the proportion of late flights (300/1000) with the probability of being from Airline B (35/100), resulting in P(B | L) = 77/300.

e) The probability that a flight is late given that it is from Airline A, denoted as P(L | A), is calculated by multiplying the proportion of flights on-time for Airline A (25/100) with the proportion of flights operated by Airline A (320/1000), resulting in P(L and A) = 8/100. Therefore, P(L | A) = 1 - P(A | L) = 11/15.

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Answer:  y = 3/2x + 1

Step-by-step explanation:  For a perpendicular line, take the reciprocal of  "m"  and reverse the sign.

- 2/3 becomes +3/2

Then substitute the y and x values of the given coordinate into the equation and solve for "b"

y = mx + b

-2 = 3/2(-2) + b

-2 = -3 + b

-2 +3 = b

+1 = b   Substitute for b in y = (3/2)x + 1

the slope of the line is 4

The result of the given equation  \((3x^2 - 2^x + 5) -(x^2 + 3x - 2)\\\) is \(4x^4-10x^3 + 14x^2\)

"Cubic polynomial is a type of polynomial based on the degree i.e. the highest exponent of the variable. Hence, a cubic polynomial is a polynomial with the highest power of the variable or degree is 3. A polynomial is an algebraic expression with variables and constants with exponents as whole numbers"

"The general form of a cubic polynomial is p(x): ax3 + bx2 + cx + d, a ≠ 0, where a, b, and c are coefficients and d is the constant with all of them being real numbers. An equation involving a cubic polynomial is called a cubic equation. "

The given equation is given as\((3x^2 - 2^x + 5) - (x^2 + 3^x - 2)\)

Solving it ,we get \(2x^2 - 5x +7\)

Now multiplying it by \(1/2x^2\) gives us \(4x^4-10x^3 + 14x^2\)

Hence the answer is \(4x^4-10x^3 + 14x^2\)

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The two numbers include 1.6682 and 4.3378 and this will give a sum of 6.006.

From the information, the sum of two numbers is 6.006 One number has a 6 in the tenths place and a 2 in the thousandths place and the other number has a 3 in the ones place and a 7 in the hundredths place.

In this case, the two numbers include 1.6682 and 4.3378 and this will give a sum of 6.006. The sum will be:

= 1.6682 +4.3378

= 6.006

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The expected value of flipping a fair coin is 0.5. This means that if we were to repeatedly flip the coin many times, the average outcome over the long run would converge to 0.5, with roughly half of the flips resulting in heads and half resulting in tails.

The expected value of a random variable is a measure of the average value or central tendency of the variable. It represents the long-term average value we would expect to observe if we repeatedly sampled from the same distribution.

As an example from my own experience, let's consider flipping a fair coin. The random variable in this case is the outcome of the coin flip, which can be either heads (H) or tails (T). Each outcome has a probability of 0.5.

The expected value of this random variable can be calculated by assigning a numerical value to each outcome (e.g., 1 for heads and 0 for tails) and multiplying it by its corresponding probability. In this case:

Expected value = (0.5 × 0) + (0.5 × 1) = 0 + 0.5 = 0.5

Therefore, the expected value of flipping a fair coin is 0.5. This means that if we were to repeatedly flip the coin many times, the average outcome over the long run would converge to 0.5, with roughly half of the flips resulting in heads and half resulting in tails.

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