What is the equation of the line in slope-intercept form? (0,4) (5,0)

Answer:

81°

Step-by-step explanation:

add both and subtract answer from 180

72+27=99

180-99=81

all 3 angles in a triangle always add up to 180°

hope this helps <3

Therefore, the maximum height to which water could be squirted with the hose, when it emerges from the nozzle, is approximately 146.86 meters.

To calculate the maximum height to which water could be squirted with the hose, we can use the principles of fluid mechanics, specifically Bernoulli's equation.

a. When the water emerges from the nozzle attached to the hose, we can assume that the velocity of water at the nozzle is the maximum, and the pressure is atmospheric pressure. At the highest point of the water stream, the velocity will be zero, and the pressure will be atmospheric pressure.

Using Bernoulli's equation, we can write:

P₁ + 1/2 ρ v₁² + ρgh₁ = P₂ + 1/2 ρ v₂² + ρgh₂

Since the water is squirting vertically upwards, the velocity at the highest point will be zero (v₂ = 0) and the pressure at the highest point will be atmospheric pressure (P₂ = P₀, where P₀ is atmospheric pressure). Also, the pressure at the nozzle (P₁) can be considered to be approximately atmospheric pressure.

The equation simplifies to:

1/2 ρ v₁² + ρgh₁ = ρgh₂

ρ is the density of water, which is approximately 1000 kg/m³.

v₁ is the velocity of water at the nozzle.

h₁ is the height of the nozzle above the ground.

h₂ is the maximum height to which water is squirted.

Since the density and the velocity are constant, we can rewrite the equation as:

v₁²/2 + gh₁ = gh₂

Solving for h₂:

h₂ = (v₁²/2g) + h₁

To calculate h₂, we need to determine the velocity v₁ at the nozzle. The flow rate through the hose and nozzle is given as 0.75 L/s. We can convert this to m³/s:

Flow rate = 0.75 L/s

= 0.75 x 10^(-3) m³/s

The flow rate (Q) is given by Q = A₁v₁, where A₁ is the cross-sectional area of the nozzle.

The cross-sectional area of the nozzle can be calculated using the radius (r₁) of the nozzle:

A₁ = πr₁²

Substituting the given radius value (0.21 cm = 0.0021 m), we have:

A₁ = π(0.0021)²

≈ 1.385 x 10⁻⁵ m²

Now we can calculate the velocity v₁:

v₁ = Q / A₁

\(= (0.75 x 10^{(-3)}) / (1.385 x 10^{(-5)})\)

≈ 54.18 m/s

Substituting the values into the equation for h₂:

h₂ = (v₁²/2g) + h₁

= (54.18² / (2 x 9.8)) + 0

= 146.86 m

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Given

To factorize.

Explanation:

It is given that,

That implies,

Hence, the answer is (2x +3a²)(2x - 3a²).

We have to find the slope of the tangent to the curve by using the definition of derivative, f′(x)= limh →0[f(x + h) − f(x)]/h, for f(x) = −15x2 + 12x + 4 and x = 5.Using the definition of the derivative, we get:f′(5) = limh →0[−15(5 + h)2 + 12(5 + h) + 4 − (−15(5)2 + 12(5) + 4)]/h= limh →0[−15h2 + 120h]/h= limh →0[−15h + 120]= −15.

Hence, the slope of the tangent to the curve at x = 5 is -15.For the second part, the equation of the tangent line at x = 5 can be found by using the point-slope form, y − y1 = m(x − x1), where m is the slope of the tangent line, and (x1, y1) is the point of tangency.Using m = −15 and (x1, y1) = (5, −295), we get:y − (−295) = −15(x − 5)y + 295 = −15x + 370y = −15x + 75.The equation of the tangent line to the curve at x = 5 is y = -15x + 75.

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Answer:

Option C

Step-by-step explanation:

Circumference of a circle is:

\(C=2\pi r\)

r - radius

We are given the radius of 3 inches.

\(C=2\pi r\\\\C=2(3)\pi \\\\C=\boxed{6\pi }\)

Option C should be the correct answer.

Hope this helps!

The domain of the function will be the value x≥-5 and the range is y ≥ -5.

The domain of a function is the set of values that can be plugged into it. This set contains the x values in a function like f. (x). A function's range is the set of values that the function can take. This is the set of values that the function returns after we enter an x value.

Given function is f(x)=1/2(x+3)²-5. The domain of the function will be all the real numbers and the range will be,

Range = 1/2(x+3)²-5

Range = 1/2(-5 + 3)² - 5

Range = 1/2(-2)² - 5

Range = -3

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i would say its the first one

\(a(1) = 240 \\ a(2) = a(1) + d = 240 + 24 = 264 \\ a(3) = a(2) + d = 264 + 24 = 288 \\ a(4) = a(3) + d = 288 + 24 = 312 \\ a(5) = a(4) + d = 312 + 24 = 336 \\ a(6) = a(5) + d = 336 + 24 = 360\)

Answer:

It already is in standard form

Step-by-step explanation:

the answer to that equation is 2 which means it's between 1 and 10. therefore it's already in standard form or "scientific notation"

After solving, the height of the cylinder is 6 meters.

The surface area of a cylinder is 24π m².

The distance around the base of the cylinder is 3π meter.

The diameter of a base of the cylinder is 4 meter.

Now the radius of the cylinder = diameter/2

The radius of the cylinder = 4/2

The radius of the cylinder = 2 meter.

The formula of surface area of cylinder:

S = 2πrh

From the question:

2πrh = 24π

Now putting the value of r

2π × 2 × h = 24π

4πh = 24π

Divide by 4π on both side, we get

h = 6

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The complete question is:

The surface area of a cylinder is 24π m². The distance around the base of the cylinder is 3π meter and the diameter of a base of the cylinder is 4 meter. What is the height of the cylinder? Enter your answer, in a simplified fraction, in the box.

Assuming the ball either goes in the hole or hits the board, the probability of getting the ball in the hole is 0.197.

Probability is the chance of an expected event happening out of many other possible events.

Probability can be 1 or zero when there is 100% certainty or uncertainty.  Otherwise, probability is always between 0 and 1 as a fractional value.

Length = 34 inches

Width = 30 inches

Area = 1,020 in² (34 x 30)

Diameter of the hole = 16 inches

Radius of the hole = 8 inches (16/2)

Area of the hole = πR² or π(d/2)²

= ²²/₇ x 8 x 8

= ²²/₇ x 64

= 201 in²

The probability of getting the ball in the hole = the area of the hole divided by the area of the board.

= 0.197 (201/1,020).

Thus, if a person tries to throw a ball in the hole, the probability of achieving intended objective is 0.197.

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The equation that represents the number of pages Ben can read per minute is p = (3/4)m.

The two quantities are said to be in a directly proportionate relation when the connection between them is such that if we increase one, the other will also increase, and if we reduce one, the other quantity will also drop.

If x and y are in direct proportion then

=>  x ∝ y

=>  x = ky  [ where k is constant ]

Here we have,

Ben reads 6 pages in 8 minutes

9 pages can be read in 12 minutes

30 pages can be read in 40 minutes

And the number of minutes = m

Number of pages = p

If observe the given data,

When the number of pages increases, the number of minutes are also increasing, So here we can conclude that the number of minutes is directly proportional to the number of pages

=> p ∝ m

=> p = km --- (1)  

[ where k is constant ]  

From the given data,

At p = 6 pages, m = 8 minutes

=> 6 = k(8)

=> k = 6/8 = 3/4

From (1)

=> p = (3/4)m

Therefore,

The equation that represents the number of pages Ben can read per minute is p = (3/4)m

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Answer:

Below

Step-by-step explanation:

4 minutes = 4  x 60 = 240 seconds

240 seconds / 15 q   = 16 s/q

Answer:

hours

Step-by-step explanation:

12 hours on an analog clock. there are 60 minutes in an hour, not 12.

To clear fractions you need to multiply both sides by same number.

This number is the least common multiplier (LCM) of both denominators.

The probability that the series lasts exactly five games is 2p raise to the power 4(1-p).

How to find probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain. The higher the probability, the more likely it is that the event will occur.

To find the probability that the series lasts exactly five games, we need to consider all possible ways in which a team can win four games in five games played.

One possible scenario is that team A wins the first four games and team B wins the fifth game. The probability of this happening is:

P(A wins the first four games and B wins the fifth game) = p⁴ * (1-p)

Another possible scenario is that team B wins the first game, team A wins the next four games. The probability of this happening is:

P(B wins the first game and A wins the next four games) = p⁴* (1-p)

Therefore, the probability that the series lasts exactly five games is the sum of these two probabilities:

P(series lasts exactly five games) = p⁴* (1-p) + p⁴ * (1-p)

Simplifying the expression, we get:

P(series lasts exactly five games) = 2p⁴(1-p)

Therefore, the probability that the series lasts exactly five games is 2p⁴(1-p).

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In linear algebra, eigenvalues and eigenvectors are fundamental concepts related to linear transformations or matrices.

Let's start with the definitions:

1. Eigenvalue: An eigenvalue of a square matrix is a scalar value that represents a special set of vectors called eigenvectors. When a matrix is multiplied by its eigenvector, the result is a scaled version of the eigenvector.

2. Eigenvector: An eigenvector of a square matrix corresponds to a nonzero vector that, when multiplied by the matrix, results in a scaled version of the original vector. The eigenvector may change direction but not its line of action.

- \(\(|\psi\rangle\)\) is a vector in a vector space.

- \(\(\langle\psi|\)\) is the conjugate transpose of the vector \(|\psi\rangle\), forming a row vector.

Properties of the projection operator \(\(\hat{P}_\psi\):\)

1. Idempotent: The projection operator is idempotent, meaning that applying it twice to a vector produces the same result as applying it once. Mathematically\(, \(\hat{P}_\psi \hat{P}_\psi = \hat{P}_\psi\).\)

2. Hermiticity: The projection operator is Hermitian or self-adjoint. This means that its conjugate transpose is equal to the operator itself: \\((\hat{P}_\psi^\dagger = \hat{P}_\psi\).\)

3. Eigenvalue and eigenvector: The projection operator has only two distinct eigenvalues: 0 and 1. The eigenvectors corresponding to the eigenvalue 1 are vectors in the subspace defined by \(\(|\psi\rangle\)\), while the eigenvectors corresponding to the eigenvalue 0 are orthogonal to the subspace.

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Answer:

I answered this for you already :)

Answer:

For the first question, your answer would be 65 degrees. The reason for this is that complementary angles add up to 90 degrees. So, 90-25= 65 degrees.

Step-by-step explanation:

For supplementary angles- 180-the angle given= ?

Answer:

the answer is Tuesday

Step-by-step explanation:

Using the binomial distribution, it is found that since the number that has the biggest absolute difference from 42.9 is 60, hence Tuesday has the most unusual observed frequency in this sample.

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The expected value of the binomial distribution is:

\(E(X) = np\)

In this problem:

For each weekday, the expected value of births is:

\(E(X) = np = \frac{300}{7} = 42.9\)

The number that has the biggest absolute difference from 42.9 is 60, hence Tuesday has the most unusual observed frequency in this sample.

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Answer:

Step-by-step explanation:

\((7+x)^5\)

If tax is 6% and tip is 15%, the total cost of the dinner, including tax and tip, is $107.99.

To find the total cost of the dinner, we need to add the tax and tip to the pre-tax amount.

The tax on the food bill can be calculated by multiplying the pre-tax amount by the tax rate of 6%, which is:

Tax = 0.06 x $89.25 = $5.355

Next, we need to calculate the tip on the pre-tax amount. The tip rate is 15%, which is:

Tip = 0.15 x $89.25 = $13.39

Now, we can calculate the total cost by adding the pre-tax amount, tax, and tip, which is:

Total cost = $89.25 + $5.355 + $13.39 = $107.995

Rounding this amount to the nearest cent gives us:

Total cost = $107.99

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Answer:

D) 88 degrees

Step-by-step explanation:

Angle ABC is 1/2Arc AC (Inscribed angle theorem)

In the illustration, there are 2 9-point stars and 8 5-point stars.

Let x be the number of 5-pointed stars and y be the number of 9-pointed stars. Each 5-pointed star has 5 points and each 9-pointed star has 9 points, so the total number of points in the drawing is:

5x + 9y = 66

There are two variables in the equation, so we need another equation to solve for x and y. The problem states that there are a total of 10 stars in the drawing, so:

x + y = 10

We can represent this system of linear equations using a matrix:

[5 9] [x] [66]

[1 1] [y] = [10]

This is a matrix equation of the form Ax = b, where A is the coefficient matrix, x is the variable matrix, and b is the constant matrix. We can solve for x and y by finding the inverse of the coefficient matrix A:

A^-1 = 1/(5-9) [-9 5]

[ 1 -1]

Multiplying both sides by A^-1, we get:

x = A^-1 b

x = 1/(5-9) [-9 5] [66]

[1 -1] [10]

x = [-3 8]

Therefore, there are 8 5-pointed stars and 2 9-pointed stars in the drawing.

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Using it's concept, it is found that there is a 0.875 = 87.5% probability that the player wins the match.

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

In this problem, these following outcomes result in the player winning the match:

Hence, the probability that he wins the match is given as follows:

p = 0.5 + 0.5² + 0.5³ = 0.875.

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Answer:

what happening to you

please answer your very

Richard's net pay for the week, considering Social Security, Medicare, and FIT deductions, can be calculated by subtracting the total deductions from his gross earnings.

First, let's determine the amount deducted for Social Security. The Social Security rate is 6.2%, and the maximum earnings subject to this deduction are $118,500. Since Richard is $1,000 below the maximum level, the amount subject to Social Security deduction is $1,000. Therefore, the Social Security deduction is 6.2% of $1,000.

Next, we calculate the Medicare deduction. The Medicare rate is 1.45%, and it is applied to the entire earnings of $1,700.

To calculate the FIT deduction, we need additional information about Richard's taxable income, tax brackets, and exemptions. Without this information, we cannot provide an accurate calculation for the FIT deduction.

Finally, we subtract the total deductions (Social Security, Medicare, and FIT) from Richard's gross earnings of $1,700 to obtain his net pay for the week.

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The probability that the two they choose will consist of each of their favorite flavors is equals to the 0.001282.

We have logan and john have a jelly bean collection. Total number of jelly bean flavors that they have = 40

They randomly select two flavors. We assume that they have different favourite flavours. That is they choose two beans of their favourite flavours.

Therefore, total number of ways to choose 2 jelly beans out of total 40 jelly beans = ⁴⁰C₂

= 40!/2!( 40 - 2)!

= 40!/38!2!

= 40×39/2

= 20 × 39 = 780

Total number of ways to choose exactly 2 jelly beans which consists their favourite flavours

= ²C₂ = 1

So, the probability that the two they choose will consist of each of their favorite flavors = total no. of favourable outcomes/total possible outcomes

= 1/780

= 0.00128205128

Hence, required probability is 0.001282.

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Different logs measure different physical properties of the formation that are related to porosity, and the relationship between the log measurement and porosity can be expressed through equations.

The different logs used to obtain porosity and their principles of measurement, quantities measured, and relation to porosity.
There are three main types of logs used to obtain porosity: neutron logs, density logs, and sonic logs.
Neutron logs: These logs measure the hydrogen content in a formation, which is directly related to porosity. The tool emits neutrons that interact with hydrogen atoms, and the resulting gamma rays are measured. The count rate decreases with increasing porosity. The neutron log can be expressed as:
Porosity = (neutron log reading - matrix reading) / (fluid reading - matrix reading)
Density logs: Density logs measure the bulk density of a formation, which can be related to porosity. The tool emits gamma rays that interact with the formation, and the scattered gamma rays are measured. The bulk density decreases with increasing porosity. The density log can be expressed as:
Porosity = (matrix density - bulk density) / (matrix density - fluid density)
Sonic logs: Sonic logs measure the travel time of sound waves through a formation, which can be related to porosity. The tool sends an acoustic wave and measures the time it takes to travel a specific distance. The travel time increases with increasing porosity. The sonic log can be expressed using Wyllie's time-average equation:
Porosity = (sonic log reading - matrix reading) / (fluid reading - matrix reading)
In summary, neutron logs measure hydrogen content, density logs measure bulk density, and sonic logs measure travel time of sound waves. These measurements can be used to calculate porosity using the respective equations provided.

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