state the mean-value theorem for derivatives. can the mean-value theorem be used to conclude that v(t) was never zero on the interval [0, ln 2]? why or why not?

Answer: The quotient is 4 52/185, which rounds to 4.

Explanation is in the image.

Answer: Actually kinda ez not gonna lie. y = 11.547, x = 23.094

Step-by-step explanation: we know that y * square root of 3 = 20. 20/ root 3 is 11.547. Hypotenuse is 2 times y. This gives us x = 23.09

The probability that the cook adds the right ingredients and cooks well is 0.75

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

Right ingredients = 9 times

Errors = 3 times

using the above as a guide, we have the following:

Total = 9 + 3

Evaluate the sum

Total = 12

The probability that the cook adds the right ingredients and cooks well is

P = Right ingredients/Total

So, we have

P = 9/12

Evaluate

P = 0.75

Hence, the probability is 0.75

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The value of a5 is 8.

Given that,

a₁ = 4

aₙ = aₙ₋₁ + 1

So, we can find the second term a₂ using the equation of nth term,

a₂ = a₍₂₋₁₎ + 1

a₂ = a₁ + 1

Applying the value of a₁,

a₂ = 4 + 1

a₂ = 5

So, finding the value of a₃,

a₃ = a₍₃₋₁₎ + 1

a₃ = a₂ + 1

a₃ = 5 + 1

a₃ = 6

So, the value of a₄ will be,

a₄ = a₃ + 1 = 6 + 1

a₄ = 7

Therefore,

a₅ = a₄ + 1 = 7 + 1

a₅ = 8

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The length of side of the rectangle is 6 mm

Since the rectangle has an area of A = 36 mm² and the rectangle has all its sides the same length, then, it is a square. We know that the area of a square A = L² where L = length of sides of square.

Since we require the length of sides of the rectangle, we make L subject of the formula.

So, L = √A

Now, since the area of the rectangle, A = 36 mm², substituting the value of the variable into the equation, we have

L = √A

L = √(36 mm²)

L = 6 mm

The length of side of the rectangle is 6 mm

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Answer:

1.8m per minute

Step-by-step explanation:

Answer:

\(\frac{1.8 \ m}{1 \ min}\) ; (1.8 meters per minute)

Step-by-step explanation:

Use dimensional analysis to solve this problem.

The proper units of conversion are given in parentheses on this question: 100 cm = 1 m.

Start with the given value, 3 centimeters/1 second.

Convert this rate to meters/minute by multiplying 3 cm/1 sec by 1 m/100 cm.

The top and bottom units should cancel out, so that's how you know to put the cm units on the bottom to cancel out with the 3 cm on the top.

Multiply the fractions together. The "cm" units cancel out.

Now you want to make the bottom units = minutes. There are 60 seconds in 1 minute, so you can use \(\frac{60 \ sec}{1 \ min}\) to multiply with \(\frac{3\ m}{100 \ sec}\).

The "seconds" unit cancels out, so you are left with meters on the top and minutes on the bottom. Multiply the fractions together.

We want the rate to be meters per minute (1), so completely simplify this fraction and divide the fraction by (100/100), so the denominator is 1 min.

Answer:

y = -x/4 + 30

y = -2x/3 + 490

Step-by-step explanation:

5x+20y=600

5x-5x+20y=-5x+600

20y=-5x+600

20y/20=(-5x+600)/20

20y/20=-5x/20+600/20

y = -x/4 + 30

2x+3y=1470

2x-2x+3y=-2x+1470

3y=-2x+1470

3y/3=(-2x+1470)/3

3y/3=-2x/3+1470/3

y = -2x/3 + 490

Answer:

2x + x2 - 3 = 0

Step-by-step explanation:

im not 100% sure if this is right but hope it helps :-)

The required equivalent equation in factored form is (x + 3)(x - 1) = 0.

A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.

Here,

We can solve for x by factoring the quadratic equation x² + 2x - 3 = 0.

To factor, we need to find two numbers that multiply to -3 and add up to 2. Those two numbers are 3 and -1, so we can write:

x² + 2x - 3 = (x + 3)(x - 1) = 0

This equation is equivalent to the original equation x² + 2x - 3 = 0.

Thus, the equivalent equation in factored form is (x + 3)(x - 1) = 0.

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Answer:

Thats a science question.

Step-by-step explanation:

b. Linear programming model is the correct option.

A linear programming model is a mathematical technique used to find the best outcome in a given set of constraints. In this case, Manders Manufacturing Corporation is trying to determine the optimal product mix for its two products, metal (M) and scrap metal (S), based on certain constraints. The objective is to maximize the profit, represented by the function Z = $30M + $70S.

The constraints are represented by the inequalities:

3M + 2S ≤ 15

2M + 4S ≤ 18

These constraints define the limitations on the production of metal and scrap metal. The model aims to find values of M and S that satisfy these constraints while maximizing the objective function.

Using linear programming techniques, the corporation can solve this model to find the optimal values for M and S that will maximize their profit. This approach allows them to make data-driven decisions and allocate their resources efficiently. By formulating the problem as a linear programming model, Manders Manufacturing Corporation can make informed choices about the optimal product mix to achieve their business objectives.

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We have two points of the line, and we have to find the equation of the line in the slope-intercept form:

First, we find the slope as:

With the value of the slope, we can calculate b replacing the values of x and y with one of the know points:

Now, we have the two parameters (slope and y-intercept) to define the line, and we can write the equation as:

Answer: They are congruent, because the angle representers are equal on both triangles

Step-by-step explanation:

Answer:

1.1 hour or 1 hour and 6 minutes

Step-by-step explanation:

Time is given by the distance divided by the velocity. If the time it takes the tugboat to travel 20 km downstream in the same time it takes it to travel 10 km upstream, then:

\(t_1=t_2\\\frac{20}{v_b+v_c}=\frac{10}{v_b-v_c}\\v_c=5\ km/h\\20v_b-100=10v_b+50\\10v_b=150\\v_b=15\ km/h\)

The velocity of the boat is 15 km/h. When traveling downstream, the current will favor the boat, therefore, the time required for it to travel 22 km downstream is:

\(t=\frac{22}{v_b+v_c} \\\t=\frac{22}{15+5}\\ t=1.1\ hour\)

It will take the boat 1.1 hour or 1 hour and 6 minutes.

Answer: 200%

Step-by-step explanation:

A radio when sold at a certain price gives a gain of 20 %.

Selling Price = 3 × Cost Price

TO FIND :- Gain percent

Gain % = gain / cp x 100

20 = (gain x 100) / cp

Gain/cp = 20/100 = 1/5

Gain = SP - CP

= 3CP - CP

Gain = 2CP

Gain% = gain / cp x 100

= 2cp / cp x 100

= 2 x 100 = 200%

Therefore, the correct answer is option D: "The wire is on the cylinder axis and carries current i in the direction opposite to that of the current in the shell. "Option E, "the wire does not carry any current," is not correct because the wire is in a region with a magnetic field, and therefore will have an induced current.

we are asked to determine the position and direction of the wire that is parallel to the cylinder axis in the hollow region. The long straight cylindrical shell has an inner radius R and an outer radius Ro, and carries a current i that is uniformly distributed over its cross section. The wire is located in the hollow region, which is defined as r > R and r < Ro.

Based on this information, we can determine the position and direction of the wire.To begin, we know that the wire must be on the cylinder axis since it is parallel to the axis. This eliminates options A, B, and C. Additionally, we know that the current in the wire must be in the opposite direction to the current in the shell. This is because the magnetic field created by the current in the shell will induce a current in the wire that is opposite in direction in order to create a repulsive force.

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Answer:

\(\boxed{\boxed{\sf 3(x+8y)}}\)

Step-by-step explanation:

\(\sf 3x+24y\)

Factor out the GCF( Write GFC first, then, in parentheses divide each term by the GCF).

GCF: → 3

\(\leadsto\sf \textsf{\:}3\left(\cfrac{3x}{3}\:+\cfrac{24y}{3}\right)\)

Simplify each term in parentheses:

\(\leadsto\sf 3(x+8y)\)

_______________________________________

Answer:

A. 3(x+8y)

Step-by-step explanation:

Just did it

Answer:

$12

Step-by-step explanation:

Half of $36 would be $18. $18 divided by 3 would be $6. $6 times 2 would be $12. Half comes from the 1/2 of money spent on Thursday. Dividing it by 3 comes from the remainder on Wednesday. We divide it by 3 since the denominator of 2/3 is 3. We then multiply it by 2, since the numerator in 2/3 is 2.

We would need to flip the coin 107 times to obtain a 90% confidence interval with a width of at most 0.16 for the probability of flipping a head.

To answer this question, we can use the formula for the margin of error in a binomial proportion confidence interval, which is:

Margin of Error = z*sqrt(p*(1-p)/n)

Here, z is the z-score corresponding to the desired level of confidence (90% = 1.645), p is the estimated probability of flipping heads (which we assume to be 0.5 for a fair coin), and n is the sample size we need to determine.

We want the margin of error to be at most 0.16, so we can plug in these values and solve for n:

0.16 = 1.645*sqrt(0.5*(1-0.5)/n)

Squaring both sides and rearranging, we get:

n = (1.645/0.16)^2 * 0.5*(1-0.5)

n ≈ 84.18

So we would need to flip the coin at least 85 times to obtain a 90% confidence interval for the probability of flipping a head with a width of at most 0.16. Note that this assumes that the coin is actually fair – if it is biased towards heads or tails, we may need a larger sample size to achieve the same level of precision.

To find the required number of coin flips for a 90% confidence interval with a width of at most 0.16, we can use the formula for the margin of error in a proportion:

Margin of Error = Z * sqrt(p * (1-p) / n)

Here, Z is the Z-score corresponding to the desired confidence level (90%), p is the suspected probability of flipping a head (0.5, since we suspect the coin is fair), and n is the number of flips we want to find.

For a 90% confidence interval, the Z-score is approximately 1.645 (you can find this from a Z-table). The margin of error is half the width of the confidence interval, so in this case, it's 0.16 / 2 = 0.08.

Now, we can plug these values into the formula and solve for n:

0.08 = 1.645 * sqrt(0.5 * (1-0.5) / n)

Squaring both sides, we get:

0.0064 = 2.706025 * (0.5 * 0.5) / n

To isolate n, we can rearrange the equation:

n = 2.706025 * (0.5 * 0.5) / 0.0064

n ≈ 106.09

Since we cannot have a fraction of a coin flip, we round up to the nearest whole number. Thus, we would need to flip the coin 107 times to obtain a 90% confidence interval with a width of at most 0.16 for the probability of flipping a head.

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The function represents the height of the plant in centimetres after n days, so n cannot be negative.

Part A:

To find a reasonable domain to plot the growth function, we need to consider the practical limitations of the growth of the plant. Also, since the function represents the growth of a particular species of plant, there may be an upper limit to how many days the plant can grow.

Assuming that the plant is not a perennial plant and has a limited lifespan, we can choose a reasonable domain for the function as [0, t], where t is the expected lifespan of the plant in days.

Since we do not have information about the expected lifespan of the plant, we can choose a reasonable value such as \(t = 365\)  (assuming it is an annual plant). So the domain for the function can be  \([0, 365]\)  .

Part B:

The y-intercept of the graph of the function f(n) represents the height of the plant when it was planted or started growing, that is, at n = 0. To find the y-intercept, we can substitute n = 0 in the equation:

\(f(0) = 15(1.02)^0 = 15\)

Therefore, the y-intercept of the graph of the function f(n) is \(15\) cm.

Part C:

The average rate of change of the function f(n) from n = 1 to n = 4 can be calculated using the formula:

average rate of change \(= [f(4) - f(1)] / (4 - 1)\)

Substituting the values in the equation, we get:

average rate of change \(= [15(1.02)^4 - 15(1.02)^1] / 3\)

average rate of change \(≈ 1.42 cm/day\)

Therefore, The average rate of change of the function f(n) from n = 1 to n = 4 represents the average daily growth rate of the plant during this period.

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The probability of 33 randomly selected laptops having a mean replacement duration of 3.5 years or fewer is roughly 0.0287, or 2.87%.

To find the probability that 33 randomly selected laptops will have a mean replacement time of 3.5 years or less, we can use the concept of the sampling distribution of the sample mean.

Given that the population means replacement time is 3.7 years and the standard deviation is 0.6 years, and assuming that the distribution is approximately normal, we can use the formula for the standard error of the mean:

Standard Error (SE) = σ / √n

where n is the sample size and σ  is the population standard deviation.

In this case, σ = 0.6 years and n = 33. Plugging these values into the formula, we get:

SE = 0.6 / √33 ≈ 0.1045

Next, we need to calculate the z-score for the sample mean of 3.5 years. The z-score formula is:

z = (x - μ) / SE

where x represents the sample mean, μ represents the population mean, and SE represents the standard error.

Plugging in the values, we have:

z = (3.5 - 3.7) / 0.1045 ≈ -1.91

Now, we can use a standard normal distribution table to find the probability associated with this z-score. The probability represents the area under the curve to the left of the z-score.

Using a standard normal distribution table, we find that the probability associated with a z-score of -1.91 is approximately 0.0287.

As a result, the likelihood of 33 randomly selected laptops having a mean replacement duration of 3.5 years or fewer is roughly 0.0287, or 2.87%.

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Answer:

x=5,4

Step-by-step explanation:

as u got 2 x to find the value of

Answer:

You must multiply the two equates so that they are opposite to each other. so you have to multiply 9 by 7 and 8 by (n-3) ).

Step-by-step explanation:

9*7=8*(n-3)

\(72 = 8n - 24\)

8n=96

n=12

Answer:

1 solution , x = 0

Step-by-step explanation:

8(x + 9) = 72 - 5x ← distribute parenthesis on left side

8x + 72 = 72 - 5x ( add 5x to both sides )

13x + 72 = 72 ( subtract 72 from both sides )

13x = 0 ⇒ x = 0

x = 0 is the only solution to the equation

We have three vertices with degrees 0, 1, and 2. When n = 4, we have four vertices with degrees 0, 1, 2, and 3.

Constructing the isomorphism types of r-regular graphs:

An r-regular graph is a graph in which every vertex has r adjacent vertices, and the degree of every vertex is r. We can easily construct a graph by connecting the vertices together with edges. The problem is to determine the number of non-isomorphic r-regular graphs for total nodes n = 1, 2, 3, 4.

Using the Havel–Hakimi algorithm, we can create isomorphism types of r-regular graphs. The Havel–Hakimi algorithm is an algorithm for determining whether a given sequence of integers is graphical, which means whether there exists a finite simple graph with that degree sequence. This algorithm works by constructing a sequence of degree-preserving graph operations. Then, we can use the algorithm to produce the isomorphism types of r-regular graphs for total nodes n = 1, 2, 3, 4. For example, when n = 1, we have one vertex with degree 0. When n = 2, we have two vertices with degrees 0 and 1. When n = 3, we have three vertices with degrees 0, 1, and 2. When n = 4, we have four vertices with degrees 0, 1, 2, and 3.

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Step-by-step explanation:

The rule for a 90-degree clockwise rotation about the origin (0,0) is:

(x,y) -----> (y,-x)

Simply apply this and you'll get your answer.

Hope this helps :)

Yes, $9 for 4 visitors and $18 for 8 site visitors are proportional.

To determine whether or not $9 for 4 visitors and $18 for 8 visitors are proportional, we need to test if the ratio of the value to the number of visitors is the equal for both cases.

The ratio of cost to the quantity of visitors for $9 and four visitors is:

$9/4 visitors = $2.25/ visitors

The ratio of value to the quantity of visitors for $18 and eight visitors is:

$18/8 visitors = $2.25/ visitors

We are able to see that both ratios are equal to $2.25 per visitor.

Therefore, $9 for 4 visitors and $18 for 8 site visitors are proportional.

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The correct answer to this question is a. The regression \(r_{2}\) is a measure of the goodness of fit of your regression line. This means that it tells you how well the regression line fits the data and how much of the variation in the dependent variable can be explained by the independent variable. In other words, it is a measure of the strength of the relationship between the two variables being analyzed.

The determinant is a mathematical term used in linear algebra that helps determine the properties of a matrix. It is not directly related to the regression \(r_{2}\) value, so option c is incorrect. Option b is also incorrect as the regression \(r_{2}\) value does not determine whether or not x causes y. Finally, option d is also incorrect as ess and tss are not related to the goodness of fit of the regression line.

Overall, the regression \(r_{2}\) value is an important measure in determining the quality of a regression model and how well it can predict outcomes based on the independent variable. It is calculated by dividing the explained variance by the total variance and is expressed as a percentage. A high \(r_{2}\) value indicates a strong relationship between the variables and a good fit of the regression line to the data, while a low \(r_{2}\) value indicates a weak relationship and a poor fit.

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Answer:

7 hours

Step-by-step explanation:

82.25/11.75 = 7

Answer:

You need to work for 7 hours

Step-by-step explanation:

You need to multiply 11.75 to 7 and you will get 82.25.

Answer:

6

Step-by-step explanation:

1 and 1/2 is equal to 1 and 2/4, or 6/4. This means that it would take 6 teaspoons to add 1 1/2 teaspoons of baking soda. hope this helps!