Find the leg and hypotenuse.

In this problem, we are dealing with a random variable related to people's opinions on a new building project. We are given four options for the correct wording of the random variable and need to determine the correct one. Additionally, we are asked to calculate probabilities associated with the number of people who favor the new building project, ranging from exactly 4 to at most 6.

a) The correct wording for the random variable is "rv = the number of people who are in favor of a new building project." This wording accurately represents the random variable as the count of individuals who support the project.

b) To calculate the probability that exactly 4 people favor the new building project, we need to use the binomial probability formula. Assuming the probability of a person favoring the project is p, we can calculate P(X = 4) = (number of ways to choose 4 out of 10) * (p^4) * ((1-p)^(10-4)). The value of p is not given in the problem, so this calculation requires additional information.

c) To find the probability that less than 4 people favor the new building project, we can calculate P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3). Again, the value of p is needed to perform the calculations.

d) The probability that more than 4 people favor the new building project can be calculated as P(X > 4) = 1 - P(X ≤ 4) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)).

e) The probability that exactly 6 people favor the new building project can be calculated as P(X = 6) using the binomial probability formula.

f) To find the probability that at least 6 people favor the new building project, we can calculate P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10).

g) Finally, to determine the probability that at most 6 people favor the new building project, we can calculate P(X ≤ 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6).

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Answer:

x = 2

Step-by-step explanation:

First subtract 3 from both sides

4x = 8

Next divide 8 by the opposite side

x = 2

Please mark as brainliest

Answer:

The answer is x = 2.

Step-by-step explanation:

Move all terms that don't contain  "x"  to the right side and solve.

Hoped this helped!

The first partial derivatives of the function f(x, y, z) = 9x sin(y - z) are fx(x, y, z) = 9 sin(y - z), fy(x, y, z) = 9x cos(y - z), and fz(x, y, z) = -9x cos(y - z).

To find the first partial derivatives, we differentiate the function with respect to each variable while treating the other variables as constants.

To find fx, we differentiate the function f(x, y, z) = 9x sin(y - z) with respect to x. Since sin(y - z) is treated as a constant with respect to x, we simply differentiate 9x, which gives us fx(x, y, z) = 9 sin(y - z).

To find fy, we differentiate the function f(x, y, z) = 9x sin(y - z) with respect to y. Using the chain rule, we differentiate sin(y - z) and multiply it by the derivative of the inner function (y - z) with respect to y, which is 1. This gives us fy(x, y, z) = 9x cos(y - z).

To find fz, we differentiate the function f(x, y, z) = 9x sin(y - z) with respect to z. Again, using the chain rule, we differentiate sin(y - z) and multiply it by the derivative of the inner function (y - z) with respect to z, which is -1. This gives us fz(x, y, z) = -9x cos(y - z).

Therefore, the first partial derivatives are fx(x, y, z) = 9 sin(y - z), fy(x, y, z) = 9x cos(y - z), and fz(x, y, z) = -9x cos(y - z).

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Answer:

68.4210526

Step-by-step explanation:

Hope this helps :)

Answer:

68.42

Step-by-step explanation:

and you can also derive that 38 percent of 68.42 equals 26.

We can determine coordinates if point t is between points u and v by checking if u < t < v or v < t < u.

To determine if point t is between points u and v, we need to compare their coordinates. If u < v, then point t is between points u and v if and only if u < t < v. On the other hand, if v < u, then point t is between points u and v if and only if v < t < u.

Whether or not point t is between points u and v depends on the relationship between the coordinates of u and v. If u < v, t must fall between them, and if v < u, t must also fall between them.

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this is:

answer: E

Answer:

12 miles

Step-by-step explanation:

Total miles = Length of trail ×

Number of times she rode

Total miles = 3 miles × 4 times

Total miles = 12 miles

Mika traveled a total of 12 miles.

A sequence of transformation that would move ΔABC onto ΔDEF is: D. a dilation by a scale factor of 1/2, centered at the origin, followed by a 90° clockwise rotation about the origin.

In Geometry, a dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.

In this scenario an exercise, we would dilate the coordinates of the pre-image by applying a scale factor of 1/2 that is centered at the origin as follows:

Ordered pair B (-4, 2) → Ordered pair B' (-4 × 1/2, 2 × 1/2) = Ordered pair B' (-2, 1).

In Mathematics and Geometry, a rotation can be defined as a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction;

(x, y)                               →            (y, -x)

Ordered pair B' (-2, 1)   →          E (1, 2)

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Answer:

The answer is 8

Step-by-step explanation:

Step 1: Calculate the circumference of the circle.

Circumference = 2πr

Where 'r' is the radius of the circle.

Since we know the center of the circle is point A, we can calculate the radius of the circle by measuring the distance from point A to any point on the circumference.

Let's say we measure the distance from point A to point B.

Radius = AB = x

Step 2: Calculate the circumference of the circle.

Circumference = 2πx

Step 3: Calculate the length of arc bcp.

We know that the length of arc bcp is 2/5 of the circumference of the circle. So,

Length of arc bcp = (2/5) × (2πx)

Length of arc bcp = (4πx)/5

Step 4: Solve for x.

To solve for x, we will rearrange the equation:

(4πx)/5 = Length of arc bcp

5 × (4πx)/5 = 5 × Length of arc bcp

4πx = 5 × Length of arc bcp

4πx = 5 × (2/5) × (2πx)

4πx = 4πx

Since both sides of the equation are equal, x = x.

Therefore, the value of x is equal to itself.

The concept of tangents, sectors, angles, the chord of a circle, and proofs are all included in the circle theorem. All points in a plane that are equally far from a fixed point are located in a circle.

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Kenneth had $125 and after deducting the expenses for the zoo, candy store, and toy shop, he would have $125 - 0.04(125 - x) - 0.2(125 - x) dollars left, where x represents the amount spent on the zoo.

Let's break down Kenneth's expenses :

Kenneth spent some money on a trip to the zoo.

Let's assume he spent x dollars on the zoo.

After this expense, he has 125 - x dollars remaining.

At the candy store, Kenneth spent 4% of the remaining money. Since 4% is equivalent to 0.04, he spent 0.04(125 - x) dollars.

After this expense, he has (125 - x) - 0.04(125 - x) dollars left.

Finally, at the toy shop, Kenneth spent 0.2 of his remaining money.

Since 0.2 is equivalent to 0.2(125 - x), he spent 0.2(125 - x) dollars.

After this expense, he has (125 - x) - 0.04(125 - x) - 0.2(125 - x) dollars remaining.

To find out how much money Kenneth has left, we need to simplify the expression:

(125 - x) - 0.04(125 - x) - 0.2(125 - x) =

125 - x - 0.04 \(\times\) 125 + 0.04x - 0.2 \(\times\) 125 + 0.2x =

125 - 0.04 \(\times\) 125 - 0.2 \(\times\) 125 - x + 0.04x + 0.2x =

125 - 5 - 25 - x + 0.24x =

(125 - 5 - 25) + (0.24x - x) =

95 + (-0.76x) =

95 - 0.76x

Therefore, Kenneth has 95 - 0.76x dollars left.

The exact amount of money he has left depends on the value of x, which represents the amount he spent on the zoo.

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Answer:

slope = -3/2

y intercept = (0,0)

equation, y = -3/2x+0

Step-by-step explanation:

y2-y1/x2-x1 = -3-3/2--2 = -6/4 = slope = -3/2

y intercept = (0,0)

Based on the provided information of speed, A) Beth gets to San Francisco first. B) The first to arrive has to wait for 20 minutes for the second to arrive.

A) To find out who gets to San Francisco first, we need to calculate the time it takes for each of them to travel the distance of 400 miles.

For Brian, we use the formula time = distance / speed:

time = 400 miles / 50 mph = 8 hours

So Brian will arrive in San Francisco at 4:00 p.m. (8:00 a.m. + 8 hours).

For Beth, we use the same formula:

time = 400 miles / 60 mph = 6.67 hours

So Beth will arrive in San Francisco at 3:40 p.m. (9:00 a.m. + 6.67 hours).

Therefore, Beth gets to San Francisco first.

B) To find out how long the first to arrive has to wait for the second, we subtract the arrival time of the first from the arrival time of the second:

wait time = 4:00 p.m. - 3:40 p.m. = 0.33 hours = 20 minutes

So the first to arrive has to wait for 20 minutes for the second to arrive.

Note: The question is incomplete. The complete question probably is: Brian leaves Los Angeles at 8:00 a.m. to drive to San Francisco, 400 miles away. He travels at a steady speed of 50 mph. Beth leaves Los Angeles at 9:00 a.m. and drives at a steady speed of 60 mph. A) Who gets to San Francisco first? B) How long does the first to arrive have to wait for the second?

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An independent basic service set (IBSS) does not consist of any access points.

In an IBSS, devices such as laptops or smartphones connect with each other on a peer-to-peer basis, forming a temporary network. This type of network can be useful in situations where there is no existing infrastructure or when devices need to communicate with each other directly.

Since an IBSS does not involve any access points, it is not limited by the number of access points. Instead, the number of devices that can be part of an IBSS depends on the capabilities of the devices themselves and the network protocols being used.

To summarize, an IBSS does not consist of any access points. Instead, it is a network configuration where wireless devices communicate directly with each other. The number of devices that can be part of an IBSS depends on the capabilities of the devices and the network protocols being used.

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Answer:

B

Step-by-step explanation:

First calculate the slope. \(\frac{y2-y1}{x2-x1}\). In this case, the slope is \(\frac{4}{5}\).

If you look at all of the answer choices, they are in slope - intercept form. This makes it easier! All you have to do is find an equation with the slope 4/5 that uses the point (4,1) or (9,5).

The standard slope intercept form for a point (a,b) is

y-b = m(x-a).

Remember that two negatives equal a positive.

Substitute in the slope for m and (4,1) or (9,5) for the point (a,b).

Answer:

y= Ix-3I    (that says absolute value btw)

Step-by-step explanation:

This is the result of starting with y = |x|, then shifting it three units to the right. Replacing x with x-3 moves the xy axis three units to the left, giving the illusion the V shaped curve moved 3 spots to the right.

We don't shift up or down since the vertex is on the x axis.

We also don't vertically compress or stretch the graph either.

Side note: the vertex for this graph is (3,0) which is the lowest point of the curve.

Answer:

Amount= $2933.2

Step-by-step explanation:

The interest of $2,500 principal earning with rate of 4%, compounded quarterly, after 4 years

A= p(1+r/n)^(nt)

P= $2500

r= 4/100= 0.04

t= 4

n = 4*4= 16

A= 2500(1+0.04/16)^(16*4)

A= 2500(1+0.0025)^(64)

A= 2500(1.0025)^64

A= 2500(1.17328)

A= 2933.2

Amount= $2933.2

Answer:

No

Step-by-step explanation:

$68 - $24 - $35 = $9

$9 < $12

Therefore, Alexa can't afford to buy a $12 shirt

Answer:

no

Step-by-step explanation:

24+35=59

59+12=71

so, it does not work

The equation of the given line is:

Slope intercept form is: y = -x + 6

Point slope form is: (y - 6) = -1(x - 0)

Standard form is: x + y = 6

The formula for the linear equation between two coordinates is:

(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)

The two coordinates are:

(0, 6) and (1, 5)

Thus:

(y - 6)/(x - 0) = (5 - 6)/(1 - 0)

This can be simplified as:

(y - 6) = -1(x - 0)

It can be further written as:

y - 6 = -x - 0

y = -x + 6

The formula for linear equation in standard form is:

Ax + By = C

Thus, we have: x + y = 6

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Answer:

5/8 of the student is buy orange juice

Answer:

Step-by-step explanation:ok so if you want too  do the the root symbl on what

Answer:

c

Step-by-step explanation:

well you can see its not negative since your subtractiing negtivees witch is just adding a possivite and 64 is unreasonable

Answer:

A

Step-by-step explanation:

Bruh

The slope of the line that divides the region bounded by the parabola \(y=5x-3x^2\)and the x-axis into two regions with equal area is 5.

To find the slope of the line that divides the region into two equal areas, we need to determine the point of intersection between the parabola and the x-axis. Since the line passes through the origin, its equation will be y = mx, where m represents the slope.

Setting the equation of the parabola equal to zero, we find the x-values where the parabola intersects the x-axis. By solving the equation\(5x - 3x^2 = 0\), we get x = 0 and x = 5/3.

To divide the region into two equal areas, the line must pass through the midpoint between these x-values, which is x = 5/6. Plugging this value into the equation of the line, we have y = (5/6)m.

Since the areas on both sides of the line need to be equal, we can set up an equation using definite integrals. By integrating the equation of the parabola from 0 to 5/6 and setting it equal to the integral of the line from 0 to 5/6, we can solve for m. After performing the integration, we find that m = 5.

Therefore, the slope of the line that divides the region into two equal areas is 5.

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Answer: Yes

Step-by-step explanation: If V=12

Then we plug in for the inequality and get 12>7

When a ladder is resting against a vertical wall and making an angle of 70° from the horizontal ground the value of e is 1.12 inches.

Given that A ladder is resting against a vertical wall and making an angle of 70° from the horizontal ground and its lower ground is 0.8 inches away from the wall. When the top of the ladder slides down by 1 inch. To find:

We are to determine the value of e and create a diagram of the problem.

As we know that a ladder is resting against a vertical wall and making an angle of 70° from the horizontal ground.

Therefore, the angle made by the ladder with the wall is 90°.

So, the angle made by the ladder with the ground will be 90° - 70° = 20°.

Let the height of the wall be "x" and the length of the ladder be "y".

So, we have to determine the value of e, which is the distance between the ladder and the wall.

Using the trigonometric ratio in the triangle, we have; Sin 70° = x / y => x = y sin 70° [1]

And, cos 70° = e / y => e = y cos 70° [2]

It is given that the top of the ladder slides down by 1 inch.

Now, the ladder makes an angle of 60° with the horizontal.

So, the angle made by the ladder with the ground will be 90° - 60° = 30°.

Using the trigonometric ratio in the triangle, we have; Sin 60° = x / (y - 1) => x = (y - 1) sin 60°[3]

And, cos 60° = e / (y - 1) => e = (y - 1) cos 60°[4]

Comparing equation [1] and [3], we get; y sin 70° = (y - 1) sin 60°=> y = (sin 60°) / (sin 70° - sin 60°) => y = 3.64 in

Putting the value of y in equation [2], we get; e = y cos 70° => e = 1.12 in

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Answer:

Step-by-step explanation:

15x+5y=8-3x

18x+5y=8⇒eqn 1

15x+5y=20y

15x-15y=0⇒eqn 2

eqn 1 * 3

 54x + 15y=24⇒eqn 3

eqn 3 + eqn 2

69x=24

x=24/69=0.3478

eqn  1⇒

    5y=8-18(24/69)

     y=1.7391/5

     y=0.3478

The solution to the system of equations is (10/3, -2).

Two or more expressions with an equal sign are defined as an equation.

The given equations are 15x + 5y = 20 and y = 8-3x.

15x + 15y = 20

Substitute y = 8-3x into the above equation:

15x + 15(8-3x) = 20

15x + 120 - 45x = 20

45x - 15x = 120 - 20

30x = 100

x = 10/3

Substitute x = 10/3 in y = 8 - 3x:

y = 8 - 3 (10/3)

y = 8 - 10

y = -2

Hence, the solution to the system of equations is (10/3, -2).

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(a) The function (hog)(t) measures combined effect of the average daily global temperature (g(t)) and  amount mean sea level rises (h(T)) on the height of the sea above current mean sea level in Cape Town at time t.

(b) The combination of functions that best describes the height of the sea above current mean sea level in Cape Town at time t is f(t) + h(g(t)). This is because f(t) represents the tidal fluctuations, while h(g(t)) accounts for the rise in mean sea level due to global temperature, providing a comprehensive description of the sea level at any given time. (c) If at time t, h'(g(t))g'(t) > 0, it implies that both the rate at which the mean sea level rises with respect to the average global temperature (h'(g(t))) and the rate of change of the average global temperature (g'(t)) are positive. This indicates that at time t, the increase in global temperature is contributing to an increase in the mean sea level. It suggests a positive correlation between rising global temperatures and the rise in mean sea level.

(d) Given that h(T) = He, where H and k are constants, we can solve for H and k using the given values of h(15) = 1 and h(16) = 2. Plugging in these values, we get the equations 1 = Hg(15) and 2 = Hg(16). Dividing the second equation by the first equation, we find that g(16)/g(15) = 2/1, which implies g(16) = 2g(15). Substituting this back into the first equation, we get 1 = Hg(15), and thus H = 1/g(15). Finally, we substitute the value of H back into the second equation to solve for k. (e) If f(t) = 60cos(4πt), then f'(t) represents the derivative of f(t) with respect to t. Taking the derivative, we get f'(t) = -240πsin(4πt). The units of f'(t) would be centimeters per day since f(t) is measured in centimeters and t is measured in days. This derivative tells us the rate of change of the sea level above mean sea level in Cape Town with respect to time. Specifically, it represents how quickly the sea level is changing at any given point in time, considering the cosine oscillations.

(f) To calculate the height of the sea above mean sea level at the start of 1 June 2022, we need the values of f(t) and g(0). Given f(t) = 60cos(4πt), we substitute t = 0 into the equation to find f(0) = 60cos(0) = 60. We are also given g(0) = 14. To calculate the height, we use the combination of functions f(t) + h(g(t)). Plugging in the values, we have f(0) + h(g(0)) = 60 + h(14). However, without information about the function h(T), we cannot determine the precise value of the height. We need additional information about h(T) to evaluate the expression fully.

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Answer

Explanation

Given the word problem, we can deduce the following information:

1. Petrolyn motor oil is a combination of natural oil and synthetic oil.

2. It contains 4 liters of natural oil for every 3 liters of synthetic oil.

To determine the amount in liters of synthetic oil needed in order to make 448 liters f petroylyn oil, we first let x be the number of portions in 448 liters of mixture. Hence, the equation would be:

Next, we solve for x:

Then, we get the amount of synthetic oil:

Answer:

500 minutes= 8.33 hr

Step-by-step explanation:

The number of hours that he works will be 8 hours and 20 minutes.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Jude arrived at work at 7:55 am and left at 4:15 pm.

Convert the time into 24 hours system. Then we have

4:15 pm = 16: 15

7:55 am = 7: 55

Then the number of hours is given as,

    16: 15

  -  7: 55

     8: 20

Then the number of hours that he works will be 8 hours and 20 minutes.

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Answer:

30/40

Step-by-step explanation:

like what the other guy said

The correct answer is 46.67%

So, According to the question

The cost price of the wardrobe given is £30

The Selling price of the wardrobe given is £44.

We need to find profit percentage

We have to use formula.

Profit percentage = \(\frac{ Selling price - cost price}{costprice}\) × 100

                               =\(\frac{ 44 - 30}{30}\) x100

                               = \(\frac{14}{30}\) x 100

                              = 14.67%                          

Hence, Jim's got profit percentage is 46.67%.

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= 46.6667%  ≈ 47%