Solve each equation. List any restrictions. Check your solutions.
12/x+11=17

Answer:

We can start by isolating the variable "h".

5 8 h + 1 1 2 = 5

Subtracting 11/2 from both sides:

5 8 h = 5 - 1 1 2

Simplifying:

5 8 h = 8 1 2

Dividing both sides by 5/8:

h = 8 1 2 ÷ 5 8

Converting the mixed number to an improper fraction:

h = (8 x 8 + 1) ÷ 5 8

h = 65/8

Now, we can convert this fraction to a mixed number:

h = 8 1/8

Brigid has already picked for 8 1/8 hours, so the amount of time needed to pick the remaining strawberries is:

5 - (1 1/2 + 5/8 x 8) = 5 - (3 5/8) = 1 3/8

Therefore, Brigid still needs to pick for 1 3/8 hours to fill 5 bushels of strawberries. The answer is 1 and 3/8 hours or 2 and 3/16 hours (if simplified).

Step-by-step explanation:

Answer:

Hi! What Exacly is the question??

Step-by-step explanation:

Answer:

8m⁵

Step-by-step explanation:

m to the 5th power = m × m × m × m × m

                                = m⁵

Then multiplied by 8 = 8 × m⁵

                                   = 8m⁵

Therefore, m to the 5th power multiplied by 8 will be represented by 8m⁵.

Answer:

$1.8

Step-by-step explanation:

9/5 = 1.8

Hope this helps! You can ask me more questions in the comments if you want! :)

Answer:

4545w

;kjbStep-by-step explanation:

uy g9

The chain rule to find du/dt: du/dt = (∂u/∂x)(dx/dt) + (∂u/∂y)(dy/dt) + (∂u/∂z)(dz/dt)
du/dt = (y/z)(4p3r4) + ((x - u)/z)(4p-3r4) + \((-xy/z^2)(-4p3r)\)Now, you can substitute the given expressions for x, y, and z to compute du/dt in terms of p, r, and t.

To use the chain rule, we need to find the partial derivatives of u with respect to x, y, and z, and then multiply them together.

∂u/∂x = y/y z = 1/z

∂u/∂y = x/z

∂u/∂z = -xy/y^2 z

Now we can apply the chain rule:

∂u/∂p = (∂u/∂x)(∂x/∂p) + (∂u/∂y)(∂y/∂p) + (∂u/∂z)(∂z/∂p)

= (1/z)(3r) + (p-3r)/(p-3r+4t)(-3) + (-xy/y^2 z)(3r)

Simplifying, we get:

∂u/∂p = (3r/z) - (3xyr)/(y^2 z(p-3r+4t))

Note: The simplification assumes that y is not equal to zero. If y=0, the function u is undefined.
To find the derivative of the function u(x, y, z) with respect to t using the chain rule, you need to find the partial derivatives of u with respect to x, y, and z, and then multiply them by the corresponding derivatives of x, y, and z with respect to t.

Given u = xy/yz and x = p3r4t, y = p-3r4t, z = p3r-4t.

First, find the partial derivatives of u with respect to x, y, and z:

∂u/∂x = y/z
∂u/∂y = (x - u)/z
∂u/∂z = -xy/z^2

Next, find the derivatives of x, y, and z with respect to t:

dx/dt = 4p3r4
dy/dt = 4p-3r4
dz/dt = -4p3r

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Answer:

13-4y

Step-by-step explanation:

Without a second equation it is impossible to give a numerical value for x, but x can be expressed in terms of y.

This equation is called a "literal equation" since there are more than one variable, but only one equation (it is not a system of equations).

Therefore, solve for x by subtracting 4y from both sides:

x+4y=13

-4y      -4y

x=13-4y

Answer:

Hi! The correct answer is x=13-4y!

Step-by-step explanation:

~Subtract 4y from both sides of the equation~

Seniors at Boston College and students in a first-semester business statistics course represent a population and a sample, respectively(C).

A population refers to the entire group of individuals or items that we are interested in studying, while a sample is a subset of the population that is selected for analysis.

In option c, the seniors at Boston College represent a population as they are the entire group of interest. On the other hand, the students in a first-semester business statistics course represent a sample because they are a subset of the population (seniors at Boston College) and are selected for analysis. So c is correct option.

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The probability of x being greater than 18 (p(x > 18)) is equal to the probability of x being less than 18 (p(x < 18)) in a normal distribution.

In a normal distribution, the probability of an event happening to the left of the mean (μ) is equal to the probability of the event happening to the right of the mean. This means that if we know the probability of x being less than 18 (p(x < 18)), we can use the property of symmetry to determine the probability of x being greater than 18 (p(x > 18)).

Since the probability distribution of x is symmetric around the mean, the area under the probability density function (PDF) to the left of the mean is the same as the area to the right of the mean. Therefore, we can say:

p(x > 18) = p(x < 18)

In other words, the probability of x being greater than 18 is equal to the probability of x being less than 18 in a normal distribution.

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If the expected frequencies are not all equal, we can determine them by using the equation enp for each individual category, where n is the total number of observations and p is the probability for the category. This equation helps us calculate the expected frequency for each category based on their probabilities and the total number of observations.

On the other hand, if the expected frequencies are equal, we can determine them by using the equation n/k, where n is the total number of observations and k is the number of categories. This equation helps us distribute the total number of observations equally among the categories when the expected frequencies are equal.

Expected frequencies do not necessarily have to be whole numbers. They can be decimals or fractions depending on the context and calculations involved.

Goodness-of-fit hypothesis tests can be left-tailed, right-tailed, or two-tailed. These different types of tests allow us to assess whether the observed data significantly deviates from the expected frequencies. The choice of the tail depends on the specific research question and the alternative hypothesis being tested.

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The equation of the plane tangent to the surface z = 3x^2 - 3y^3 at the point (2, 1, 15) is 12x - 9y + z - 30 = 0.

To find the equation of the plane tangent to the surface z = 3x^2 - 3y^3 at the point (2, 1, 15), we can use the concept of partial derivatives and the equation of a plane.

1. Compute the partial derivatives of the surface equation with respect to x and y. Taking the partial derivative with respect to x treats y as a constant, and vice versa. For the given equation, we have:

  ∂z/∂x = 6x

  ∂z/∂y = -9y^2

2. Substitute the coordinates of the point (2, 1, 15) into the partial derivatives:

  ∂z/∂x = 6(2) = 12

  ∂z/∂y = -9(1)^2 = -9

3. The normal vector of the plane is obtained by taking the coefficients of the partial derivatives:

  Normal vector = (12, -9, 1)

4. Now, we have the normal vector and a point on the plane (2, 1, 15). Using the equation of a plane, which is of the form Ax + By + Cz = D, we can substitute the values:

  12(x - 2) - 9(y - 1) + (z - 15) = 0

  12x - 24 - 9y + 9 + z - 15 = 0

  12x - 9y + z - 30 = 0

Therefore, the equation of the plane tangent to the surface z = 3x^2 - 3y^3 at the point (2, 1, 15) is 12x - 9y + z - 30 = 0.

The equation represents a plane that is tangent to the given surface at the specified point. The coefficients in the equation correspond to the components of the normal vector, and the constant term is determined by evaluating the equation at the given point.

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At t = 0.4, the velocity of the particle is zero. This indicates that the particle is momentarily at rest at this time.

To determine whether there is a time interval during which the particle is not moving, we need to examine the velocity of the particle. The velocity of the particle is the derivative of its position with respect to time.

The given position function is y = 0.20 + 8.0t - 10t^2.

To find the velocity function, we take the derivative of the position function with respect to time (t):

v(t) = d/dt (0.20 + 8.0t - 10t^2)

= 8.0 - 20t

The velocity function v(t) represents the rate of change of the position of the particle with respect to time. If the velocity is zero at any point in time, it means the particle is momentarily at rest.

Setting the velocity function equal to zero, we have:

8.0 - 20t = 0

Solving for t, we find:

20t = 8.0

t = 0.4

So, at t = 0.4, the velocity of the particle is zero. This indicates that the particle is momentarily at rest at this time.

Therefore, there is a time interval during which the particle is not moving, specifically at t = 0.4. Before and after this time point, the particle is in motion either upward or downward along the y-axis.

It's worth noting that we should consider the full domain of the position function (y) to determine if there are any other time intervals during which the particle is not moving. In this case, the given function does not specify any constraints on time, so the time interval t = 0.4 is the only time interval during which the particle is at rest.

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Answer:

40 feet deep

Step-by-step explanation:

:))

Answer: $262.50

Step-by-step explanation:

Answer: There were 99 more skateboarders than skaters at the park on Saturday.

Step-by-step explanation:

Let there were 8x skaters and 3x skateboarders on Friday.

There were 168 skaters on Friday.

So, \(8x=168\)

\(\Rightarrow\ x=\dfrac{168}{8}=21\)

3x = 3 (21)=63

Total skaters and skateboarders on Friday = 168+63 =  231

Also, the  ratio of the number of skaters to the number of skateboarders was 2:5

Let there were 2x skaters and 5x skateboarders on Saturday.

Then,

\(2x+5x= 231\\\\\Rightarrow\ 7x = 231\\\\\Rightarrow\ x=\dfrac{231}{7}\)

\(\Rightarrow\ x=33\)

Number of skaters = 2(33) = 66

Number of skateboarders = 5(33) = 165

Difference = 165-66= 99

Hence, there were 99 more skateboarders than skaters at the park on Saturday.

When six integers are chosen from the set A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, there must be at least one pair of integers that adds up to 11. This can be proven using a proof by contradiction.

To solve this problem, we can use a proof by contradiction. We assume that there are six integers chosen from A such that no two integers add up to 11.

If there is no pair of integers in the six chosen that sum up to 11, then we can consider the pairs of integers (1,10), (2,9), (3,8), (4,7), and (5,6). These are the only possible pairs of integers in A that add up to 11.

However, since there are five pairs and we can choose at most one integer from each pair, we can choose at most five integers in total. This is a contradiction since we were asked to choose six integers from A. Therefore, our assumption that there are no pairs of integers that add up to 11 is false.

Hence, we conclude that there must be at least one pair of integers among the six chosen that adds up to 11.

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The parametrization for the portion of the surface given by log(y) = √(x²+z²) in the first octant is x = rcosθ, y = er, z = rsinθ with the domain 0 ≤ r < ∞ and 0 ≤ θ ≤ π/2.

To sketch and find a parametrization for the portion of the surface given by log(y) = √(x²+z²) in the first octant, we can use a cylindrical coordinate system.

First, let's consider the domain of the parametrization. Since we are in the first octant, all coordinates must satisfy x ≥ 0, y ≥ 0, and z ≥ 0.

Now, let's introduce cylindrical coordinates:

x = rcosθ

y = y

z = rsinθ

Substituting these into the equation log(y) = √(x²+z²), we get:

log(y) = √((rcosθ)² + (rsinθ)²)

log(y) = √(r²(cos²θ + sin²θ))

log(y) = √(r²)

log(y) = r

Therefore, we have the parametrization:

x = rcosθ

y = er

z = rsinθ

The domain of this parametrization is: 0 ≤ r < ∞, 0 ≤ θ ≤ π/2.

To sketch the surface, we can choose different values for r and θ within the given domain and plot the corresponding points (x, y, z). This will generate a curve in 3D space that represents the portion of the surface in the first octant.

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To figure how many paths there are from (0,0) to (50,50) on a Cartesian coordinate system is using the legal moves, move up and move right. The formula that can be used is ((x+y)¦x). Here the steps;

Each path from point (0,0) to (50,50) will contain 50 rightward steps (i.e. progressive along the x-axis) and 50 upward steps (progressive along y-axis), resulting in a total of 100 steps, therefore we have ((x+y)¦x)= ((50+50)¦50) = (100¦50) ways of creating such a path.

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Answer:

Step-by-step explanation:

This is a binomial problem where the basketball player has a probability of success of 0.725 (making a free throw) and is attempting 60 shots. The number of successful shots is a binomial random variable X ~ Bin(60, 0.725). We need to find the probability that she makes at least 15 of her next 60 shots, which is P(X ≥ 15). This can be computed using the binomial cumulative distribution function (CDF) as follows:

P(X ≥ 15) = 1 - P(X < 15) = 1 - binom.cdf(14, 60, 0.725) ≈ 0.998

Therefore, the probability that she makes at least 15 of her next 60 shots is approximately 0.998.

This is also a binomial problem where the probability of success is 0.14 (a smartphone requiring servicing) and the number of trials is 100 (smartphones in a shipment). We need to find the probability that no more than 10 smartphones in the shipment will require servicing, which is P(X ≤ 10). This can be computed using the binomial CDF as follows:

P(X ≤ 10) = binom.cdf(10, 100, 0.14) ≈ 0.289

Therefore, the probability that no more than 10 smartphones in the shipment will require servicing is approximately 0.289.

This is also a binomial problem where the probability of success is 0.06 (a scratch-off lottery ticket having a prize of a free ticket) and the number of trials is 200 (tickets at the local convenience store). We need to find the probability that this prize is on 15 or more of the tickets, which is P(X ≥ 15). This can be computed using the binomial CDF as follows:

P(X ≥ 15) = 1 - P(X < 15) = 1 - binom.cdf(14, 200, 0.06) ≈ 0.021

Therefore, the probability that the prize is on 15 or more of the 200 tickets at the local convenience store is approximately 0.021.

Answer:

y = -1

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

To find slope we look for the rise/run or (y2 - y1) / (x2 - x1)

The slope here is 0, and the y-intercept is located at (0,-1), so the equation is

y = -1

Answer:

y = -1

Step-by-step explanation:

The complex number (1 + 2i) - (-2 + 16) can be expressed in Euler form as -1.29e^(7.28i).(option B).

To express the given complex number in Euler form, we first simplify the expression: (1 + 2i) - (-2 + 16) = 3 - 2i. Next, we can write the complex number in polar form by finding the magnitude (r) and argument (θ) of the complex number. The magnitude r is given by r = sqrt(3^2 + (-2)^2) = sqrt(13). The argument θ can be calculated as θ = arctan(-2/3). Finally, we can express the complex number in Euler form as -1.29e^(7.28i), where -1.29 is the magnitude (r) multiplied by the cosine of the argument (θ), and 7.28 is the sine of the argument (θ).

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Answer:

120  bud

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

\(\frac{3}{12}\) x 100 = 25%

A carton contains a dozen eggs, of which 3 contain no yolk. If 3 eggs are chosen then the probability that they all have no yolk is 3/12

Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

A carton contains a dozen eggs, of which 3 contain no yolk. If 3 eggs are chosen at random for a cake.

one dozen eggs = 12 eggs

The probability that they all have no yolk = 3/12

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The probability of drawing a ticket with value 2 when the first ticket drawn is 5 is 2/7.

The tree diagram makes it easier to arrange and see all of the potential possibilities. The tree's branches and ends are its two primary locations. On each branch is written the probability, and the ends hold the results in the end. To determine when to multiply and when to add, use tree diagrams.

Let A be an event: the first ticket extracted was the 5.

Let B be an event: the second ticket is 2.

The probability for the following is given as:

P (B/ A) = 2/7

Hence. the probability of drawing a ticket with value 2 when the first ticket drawn is 5 is 2/7.

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Since the probabilities must add up to 1, we have to solve this equation :

1/5 + 1/5 + 1/2 + x = 1

2/5 + 1/2 + x = 1

4 / 10 + 5 / 10 + x = 1

9/10 + x = 1

x = 1 - 9/10

x = 10/10 - 9/10

x = 1/10

So the value of x is 1/10

Option A is correct, the value of x should be 1/10.

It is a branch of mathematics that deals with the occurrence of a random event.

In a valid probability distribution, the sum of all probabilities must be equal to 1.

We know that the given probability distribution is 1/5, 1/5, 1/2, x. Therefore, we can write an equation:

1/5 + 1/5 + 1/2 + x = 1

Simplifying the equation, we get:

2/5 + x = 1/2

Subtract 2/5 from both sides

x=1/2-2/5

x=5-4/10

x=1/10

Hence, option A is correct, the value of x should be 1/10.

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Answer:

sam and eric are going on a trip and thought to rent a car. they have to pay a fee of 30 dollars and an extra 7 dollar for each hour they take. sam and eric's are planned to spend $205 or less. how many hours can eric and sam rent the car?

Step-by-step explanation:

first assign a value for the variable, I will take H as hours

Answer:

Sorry i dont know

Step-by-step explanation:

Answer:

1/3 min ( = 20 seconds)

Step-by-step explanation:

The period of the ride is the time he takes to complete 1 revolution

We are given:

12 revolutions -------> takes 4 min

1 revolution ------> takes 4/12 = 1/3 min  (= 20 seconds)

The type of measurement scale used by the ice festival committee to measure the depth of the ice during the month of February is the ratio scale. Here option A is the correct answer.

A ratio scale is a type of measurement scale that possesses all the properties of an interval scale with an additional feature of a true zero point. This means that the measurements on a ratio scale have a meaningful zero point, indicating the complete absence of the measured quantity. For example, in the case of measuring the depth of the ice, a ratio scale would allow us to say that the depth of the ice is zero when there is no ice present.

In contrast, interval scales, which are commonly used in temperature measurements, do not have a true zero point. While zero on an interval scale represents the absence of a particular value, it does not imply that the quantity being measured is absent altogether.

Nominal scales, on the other hand, are used to categorize data into distinct and separate groups without any inherent order or numerical value. These scales are used to measure qualitative variables, such as gender or race.

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Complete question:

During the winter, the ice festival committee measures the depth of the ice during the month of February. what is the type of measurement scale? multiple choice

A - ratio

B - interval

C - nominal

D - numerical

Answer:

0,1,2,3 is the domain

-2,1,2,4 is the range