4x+a=4x+3. How do you get to 6? Please explain and write down like you would write on paper. ​

the height of the wall is approximately 84.5 feet, rounded to the nearest tenth of a foot.

We should use the tangent function for this problem.

Let h be the height of the wall. Then we have:

tan(52 degrees) = h / 62

Solving for h, we get:

h = 62 * tan(52 degrees) ≈ 84.5 feet

what is tangent?

In trigonometry, tangent (often abbreviated as tan) is a trigonometric function that relates the ratio of the length of the opposite side to the length of the adjacent side of a right triangle. It is defined as the ratio of the sine of an angle to the cosine of the same angle:

tan(θ) = sin(θ) / cos(θ)

where θ is the measure of an angle in radians or degrees.

Tangent is commonly used to find the measure of an unknown side or angle of a right triangle when given the measure of one side and one acute angle. It is also used in many real-world applications, such as in navigation, surveying, and engineering, to determine the angle of elevation or depression, as well as in calculus to find the slope of a curve at a given point.

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When diameter is 60 mm, the volume increases at a rate of 22,620 mm³/s.

Step 1: Create an equation that connects a sphere's volume to radius as the first step.

V = 4/3*π*r³

Step 2: Calculate each side's derivative in respect to time (Let the time be "t").

(d/dt)V = (d/dt)(4/3*π*r³)

dV/dt = 4πr²*dr/dt

Step 3: The problem description informs us that the diameter is 600 m, hence r must be 30 mm.

Additionally, it is stated that now the radius of a sphere is expanding at a rate of 2 mm/s; as a result, dr/dt must equal 2 mm/s.

We are interested in dV/dt, or the rate of change of the sphere's volume.

dV/dt = 4π(30mm)²*(2mm/s)

dV/dt = 22,620 mm³/s

So, when diameter is 60 mm, the volume increases at a rate of 22,620 mm³/s.

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Answer: 34.22

Find 41% of 58 first.

\(58*0.41=23.78\)

The problem asks to decrease it, meaning you would subtract the percentage from 58.

\(58-23.78=34.22\)

34.22

Answer:

the awnser is -3

Step-by-step explanation:

Answer:

Step-by-step explanation:

-2/3(-3b-24) = 2(b+8)

6b/3+48/3 = 2b+16

2b+16 = 2b+16 => equivalent

Is -2/3(-12b-6+9b-18) equivalent to 2(b+8)?

To find out, simplify the left side.

Multiply every term in the parentheses by 2/3.

(8b + 4 - 6b + 12)

Simplify.

(2b + 16)

Factor out 2.

2(b + 8)

We conclude that -2/3(-12b-6+9b-18)

equals 2(b + 8).

Answer:

hello,

Step-by-step explanation:

y=k(x-a')²+b'

focus is (a',1/(4k)+b')

2x²=-120y

==> y=-2/120x²

==> y=-1/60(x-0)²+0

focus= (0,-15)

Answer:

714

Step-by-step explanation:

So lets go over what we know.

The bus only goes for 6 hours each day.

So lets just think of a full day as 6 hours.

Each day(6 hours), 4284 passangers ride the bus.

To find passangers per hour, we must divide the total passangers by the total hours.

This is 4284(total passangers) divided by 6(total hours):

4284/6

=

714

So each hour, there are 714 passangers.

Hope this helps!

The probability that all coins show heads up is 1/16.

The probability of one is 1/2: Half of the time (on average, as all numbers in this answer will be) it will show heads.

Of those times it shows heads, only half of the time will the second coin also show heads. We're down to a quarter of the time now.

Of those times the second coin shows heads, only half of the time will the third coin also show heads. This is 1/8.

And, of the times the third coin also shows heads, only half of the time will the fourth coin also show heads. Half of 1/8 is 1/16.

You can simplify this by calculating (1/2)^4.

= 1/16

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Take all coins that are still on tails and keep flipping them until they land on heads. We flip 4 coins simultaneously. What is the probability that all coins show heads up?

Using trigonometric ratio, the length of BE is 10 units, the value of sin B is 0.64 and cos B is 0.64 respectively

This is the ratio between the angles and sides of a right-angle triangle. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

In this problem, we have that

1)

Using tangent of B

tan B = opposite / adjacent

tan B = NE / BE

3/4 = 7.5 / BE

BE = 7.5 / 0.75

BE = 10

2)

To find sin B, we need to calculate the hypothenuse of the triangle which we will use Pythagoras's theorem

NB² = BE² + NE²

NB² = 10² + 7.5²

NB = 12.5

sin B = NE / NB

sin B = 7.5 / 12.5

B = sin⁻¹ (7.5 / 12.5)

B = 0.64

3)

cos B = BE / NB

cos B = 10 / 12.5

B = cos⁻¹ (10/12.5)

B = 0.64

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a. Area of the triangle is increasing at a rate of 16 m^2/s

b. Area of the triangle is increasing at a rate of 12√2 m^2/s

c. Length of the hypotenuse is increasing at a rate of approximately 5.66 m/s.

Since it is an isosceles right triangle

x^2 + x^2 = h^2

x√2 = h.

The area of the triangle is A = (1/2) x^2 = 8 m^2. Use the chain rule:

dA/dt = dA/dx * dx/dt

Differentiating with respect to x:

A = (1/2) x^2

dA/dx = x

So  x = 4:

dA/dt = dA/dx * dx/dt = 4 * 4 = 16 m^2/s

Area of the triangle is increasing at a rate of 16 m^2/s

h = 6 and x = 6/√2.

The area of the triangle is

A = (1/2) x^2 = 18 m^2.

Using the chain rule as before:

dA/dt = dA/dx * dx/dt

By differentiating :

A = (1/2) x^2

dA/dx = x

dA/dx = 6/√2.

dA/dt = dA/dx * dx/dt = (6/√2) * 4 = 12√2 m^2/s

Area of the triangle is increasing at a rate of 12√2 m^2/s

Differentiating the formula with respect to time:

d/dt (x√2) = d/dt (h)

dx/dt * √2 = dh/dt

dh/dt = dx/dt * (√2)

dh/dt = 4 m/s * (√2) ≈ 5.66 m/s

Length of the hypotenuse is increasing at a rate of approximately 5.66 m/s.

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During assignment, the result of the calculation on the right side of an equals sign is assigned to a variable on the left of the equals sign. Where as, equality is a logical test that evaluates whether two values are equivalent.

In the given question, the first option is correct among the four.

An assignment operator assigns the result of the calculation on the right side of an equals sign to a variable on the left of the equals sign. It is indicated by ' = '.

Example: s = 4 + years, then the operator assigns the value of the sum of 4 and years to the variable s.

On the other hand, equality is a logical test that evaluates whether two values are equivalent or not. It is indicated by ' == '. The results obtained by this operator is either true or false.

Example: If f == s, it checks whether the value stored in f equals the value stored in s. If they are equal it returns output as true else false.

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(a) The expression that represents the position of the fish relative to sea level after it rises 7.8 feet  is 13.52-7.8 = 5.72 , and

(b) The position of fish after rising 7.8 feet will be 5.72 feet below the sea level .

In the question ,

it is given that

fish swims 13.52 below  the sea level ,

original depth = 13.52 feet

fish rises by 7.8 feet relative to the sea level

Part(a)

Since the fish has risen 7.8 feet ,

so , the risen height 7.8 feet will be subtracted from original depth 13.52 feet

the expression becomes 13.52 - 7.8 = 5.72  .

Part(b)

The position of fish after it rises 7.8 feet is calculated using

= 13.52 - 7.8

Subtracting 7.8 from 13.52 we get

= 5.72

Therefore , (a) The expression that represents the position of the fish relative to sea level after it rises 7.8 feet  is 13.52-7.8 = 5.72 , and

(b) The position of fish after rising 7.8 feet will be 5.72 feet below the sea level .

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Answer:

30 students

Step-by-step explanation:

18 divided by 3 is 6

6 x 2 = 12

12 + 18 = 30

Answer:

30 i just took the test 28m ago and it said it was right

Step-by-step explanation:

To find the probability that the sample mean will lie between 78 and 81, we need to calculate the z-scores corresponding to these values and then use the standard normal distribution to determine the probability.

The Central Limit Theorem states that when the sample size is large enough, the distribution of sample means will be approximately normally distributed, regardless of the shape of the population distribution. In this case, since the sample size is 64 (which is considered large), we can assume that the sample mean follows a normal distribution.

To calculate the probability, we first convert the sample mean values of 78 and 81 into z-scores using the formula:

z = (x - μ) / (σ / √n)

where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

For 78:

z = (78 - 80) / (10 / √64) = -2 / 1.25 = -1.6

For 81:

z = (81 - 80) / (10 / √64) = 1 / 1.25 = 0.8

We can then use a standard normal distribution table or a calculator to find the probability associated with these z-scores. The probability that the sample mean will lie between 78 and 81 is the difference between the cumulative probabilities corresponding to these z-scores.

P(78 ≤ x ≤ 81) = P(-1.6 ≤ z ≤ 0.8)

Using a standard normal distribution table or calculator, we can find the cumulative probabilities associated with these z-scores and calculate the probability.

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The no two distinct tuples map to the same integer. Thus, S is countable.

(a) The issue with the first proof is that the function mapping each tuple to the sum of its elements is not injective (one-to-one).

Different tuples can have the same sum, e.g., (1, 2) and (3) both map to 3, causing a violation of the injective property.
(b) The problem with the second proof is that the function is not injective either. Tuples like (10, 2) and (1, 02) both map to 1002, which again violates the one-to-one property.
(c) To show that S is countable, we can adapt the proof in part (b) by using a different base. Instead of base 10, let's use base p (a prime number greater than the maximum integer in the tuples). We can map each tuple (a_1, a_2, ..., a_n) to the integer

\( (p^(a_1 - 1)) * (p^(a_2 - 1 + p)) * ... * (p^(a_n - 1 + (n-1)p)).\)

This function is injective because each element in the tuple uniquely contributes to the resulting integer, ensuring that no two distinct tuples map to the same integer. Thus, S is countable.

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The agent sold the vegetables for Rs. 110000

What is Selling price?

The selling price is the amount paid by a buyer for a product or service.

Let P be the price of the vegetables that the agent sold.

We know that the agent's commission is 2% of the selling price, so the commission can be represented by the equation:

Commission = (2/100) * P = 2% * P = 0.02 * P

We also know that the commission is Rs 2,200, so we can set up the equation:

0.02 * P = 2200

To find the price of the vegetables, we can solve for P by dividing both sides of the equation by 0.02:

P = 2200 / 0.02

  = 2200 / 0.02 * 100/100

  = 2200 * 100/2

P = 110000

So, The agent sold the vegetables for Rs. 110000

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The statement about an Excel table that is true is "It can be changed to a data range."

An  Excel table is a range of cells that contain related data. You may use it to create and manage a range of data in a structured and organized manner. Excel tables offer a lot of benefits, including powerful filtering, sorting, and formatting options.Excel tables can be changed to a data range, which means that the table no longer has the formatting and filtering options available to it. It transforms into a conventional data range that you can utilize in Excel.

Converting an Excel table to a data range is quite simple. The following are the steps:

Select any cell inside the table to be converted to a range.

On the ribbon, choose the Table Design tab.

Click on the Convert to Range button in the Tools group.

Click on the Yes button when the Convert Table to Range dialog box displays.

Note that all table data, formulas, and formatting will be preserved. Choose the OK button. It is true that an Excel table can be changed to a data range, so that is the correct answer.

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The distance the foot of the ladder is from the wall, to the nearest foot is

the angle the ladder makes with the house, to the nearest degree is

Information from the question

Ladder length = 20 ft

wall height = 19.5 ft

The distance the foot of the ladder is form the wall is worked using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The angle is calculated using cos, CAH let the angle be x

cos x = 19.5 / 20

x = arc cos (19.5/20)

x = 12.84 degrees

x = 13 degrees

The distance is calculated using sin, SOH, let the distance be y

sin 12.84 = y / 20

y = 20 x sin 12.84

x = 4.44 ft

x = 4 ft

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Answer:

The bill was $36.95 without tax.

The price before tax was the amount of $37.25 which is before a 9% sales tax was added to their bill.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.

Their bill was charged a 9% sales tax.

Amy paid the bill with a $10 gift certificate plus $30.60

Use the equation P + rP =T,

where P is the price before tax, r is the sales tax rate, and T is the total price, including tax.

The price before tax (P) is unknown.

The total price(T) = 30.60 + 10 = 40.60

The sales tax rate (r) = 9% = 9/100 = 0.09

⇒ P + rP = T

Substitute the values in the above equation, and we get

⇒ P + (0.09)P = 40.60

⇒ P(1 + 0.09) = 40.60

⇒ P(1.09) = 40.60

⇒ P = 30.60/(1.09)

Apply the Division operation, and we get

⇒ P = 37.247706

Rounded to the nearest hundredth

⇒ P = 37.25

Therefore, the price before tax was the amount of $37.25.

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To determine the values of the constants a and b such that the line 2x + y = b is tangent to the parabola y = ax^2 at x = 2, we need to find the points of tangency between the line and the parabola.

First, let's substitute x = 2 into the equation of the parabola to find the corresponding y-coordinate:

\(y = a(2)^2\)

y = 4a

Now, substitute x = 2 into the equation of the line to find the corresponding y-coordinate:

2(2) + y = b

4 + y = b

y = b - 4

Since the line and the parabola are tangent at x = 2, their y-coordinates at this point should be equal. Therefore, we have:

4a = b - 4

Now, let's find the slope of the tangent line. The slope of the tangent line to the parabola at x = 2 is the derivative of the parabola's equation evaluated at x = 2:

y' = 2ax

y' = 2a(2)

y' = 4a

The slope of the line 2x + y = b is determined by rearranging the equation in slope-intercept form:

y = -2x + b

Comparing the slopes, we have:

4a = -2

Now we can solve for a:

4a = -2

a = -2/4

a = -1/2

Substituting the value of a into the equation 4a = b - 4, we can find b:

4(-1/2) = b - 4

-2 = b - 4

b = -2 + 4

b = 2

Therefore, for the line 2x + y = b to be tangent to the parabola y = ax^2 at x = 2, the values of the constants are a = -1/2 and b = 2.

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Answer:

Kenjii can use 13.19 kilowatt-hour.

Step-by-step explanation:

Giving the following information:

Kenji's electricity bill costs $21.56 per month plus $2.46 per kilowatt-hour.

First, we will structure the total cost formula:

Total cost= 21.56 + 2.46*x

x= kilowatt-hour

54= 21.56 + 2.46x

32.44= 2.46x

13.19= x

Kenjii can use 13.19 kilowatt-hour.

Answer:

B. Homeowners pay additional property taxes

Step-by-step explanation:

The probability that the sample proportion (the proportion living in the dormitories) is at least 0.70 is approximately 0.02. This is option A

Let p be the sample proportion living in the dormitories.The mean of the sample proportion is given by:μp = p = 0.60.

The standard deviation of the sample proportion is given by:σp = sqrt(p(1-p)/n)=sqrt(0.6*0.4/80)= 0.049.The sample size n = 80.

From Chebyshev' s theorem: P(|X - μ| ≥ k.σ) ≤ 1/k².

Substituting μ.p = 0.60 and σ.p = 0.049, we have:P(|p - 0.60| ≥ k*0.049) ≤ 1/k².

The question asks us to find the probability that the sample proportion (the proportion living in the dormitories) is at least 0.70.

So, we have:p ≥ 0.70 = 0.60 + k*0.049, k = (0.70 - 0.60)/0.049 = 2.04

.Substituting k = 2.04 in the above expression, we have:

P(|p - 0.60| ≥ 2.04*0.049) ≤ 1/(2.04)²= 0.2362.

So, P(p ≥ 0.70) = P(p - 0.60 ≥ 0.10)= P(p - 0.60/0.049 ≥ 2.04)= P(Z ≥ 2.04)≈ 0.0207.

Hence, the probability that the sample proportion (the proportion living in the dormitories) is at least 0.70 is approximately 0.02.

So, the correct answer is A

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Answer:

Step-by-step explanation:

C. 28

5 raised to 2nd power is 25 so 25+3=28

The scientist descends from 83 feet below sea level to 151 feet below sea level, a change in depth of 151 - 83 = 68 feet. This change occurs over a time of 5 seconds.

The rate of change in depth, or the speed at which the submarine is descending, is given by the ratio of the change in depth to the time taken:

Rate of change in depth = (final depth - initial depth) / time taken

Rate of change in depth = (151 ft - 83 ft) / 5 s

Rate of change in depth = 13.6 ft/s (rounded to one decimal place)

Therefore, the rate of change in the submarine's elevation is 13.6 feet per second.

Answer: (-2,4)

Step-by-step explanation:

A solution is an intersection point between the parabola and the linear function. We can see 2 intersections, one of which is (-2,4)

Therefore, (-2,4) is the solution.

Answer:

-6z

Step-by-step explanation:

Answer:

−6z is your answer

Step-by-step explanation: