Smith and his friends are gaming online on a popular website. An hour later, 6 friends go offline. Five of them continue playing. How many of them were gaming online initially?

Write the problem__

People on line originally

The value of x where f′(x)=3 is 5/3.

Let f(x)=x+4x.

To find the values of x where f′(x)=3, we first find the derivative of f(x).

f(x) = x + 4x f'(x) = 1 + 4 = 5

Given that f'(x) = 3, we can now solve for x using the following equation:

5 = 3x => x = 5/3

Therefore, the value of x where f′(x)=3 is 5/3.

To summarize, we used the formula for derivative and then set it equal to 3.

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Answer:

The slope is 5

Step-by-step explanation:

y - 3 = 5(x - 2)

Distribute;

y - 3 = 5x - 10

Add 3 to both sides;

y = 5x - 7

Answer:

Step-by-step explanation:

The y-intercept is (0,1).

Answer: The answer is A

Step-by-step explanation:

12 is NOT a multiple of 8. She only listed multiples for 12 not 8.

Answer:

the anwer is a

Step-by-step explanation:

some of the numbers were not factors

The thickness of the clay layer, which drains only from the upper surface, can be determined based on the consolidation settlement observations. With 50% of consolidation settlement occurring in 1 hour for a 25 mm thick specimen, and a total primary consolidation settlement of 35 mm occurring over many years, the thickness of the clay layer is approximately 87.5 mm.

The consolidation settlement of a clay specimen can be used to estimate the thickness of a clay layer that drains only from the upper surface. In this case, the observed settlement data provides valuable information.

Firstly, we know that 50% of the consolidation settlement occurs in 1 hour for a 25 mm thick clay specimen. This is an important parameter for calculating the coefficient of consolidation (Cv) using Terzaghi's theory. From the Cv value, we can estimate the time required for full consolidation settlement.

Secondly, we are given that the same clay settles 10 mm over 10 years and eventually settles a total of 35 mm over a longer period. This long-term settlement is known as the total primary consolidation settlement. By comparing this settlement value with the settlement data from the oedometer test, we can determine the thickness of the clay layer.

To calculate the thickness, we can use the concept of the consolidation settlement ratio. The ratio of the total primary consolidation settlement to the consolidation settlement at 50% completion is equal to the ratio of the total thickness to the thickness at 50% completion. Applying this ratio, we can determine that the thickness of the clay layer, which drains only from the upper surface, is approximately 87.5 mm.

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Using the cosine formula for a difference, we can prove the identity cos(3π/2 - θ) = -sin(θ) by setting a = 3π/2 and b = θ. Simplifying the equation, we get cos(3π/2 - θ) = 0*cos(θ) + (-1)*sin(θ), which equals -sin(θ).

To establish the identity cos(3pi/2 - theta) = -sin theta, we will use the formula for the cosine of a difference:

cos(a - b) = cos(a)cos(b) + sin(a)sin(b)

Let a = 3pi/2 and b = theta. Then we have:

cos(3pi/2 - theta) = cos(3pi/2)cos(theta) + sin(3pi/2)sin(theta)

Now, cos(3pi/2) = 0 and sin(3pi/2) = -1, so we can simplify this to:

cos(3pi/2 - theta) = 0*cos(theta) + (-1)*sin(theta)

cos(3pi/2 - theta) = -sin(theta)

Therefore, we have established the identity cos(3pi/2 - theta) = -sin theta.

To establish the identity cos(3π/2 - θ) = -sin(θ), we can use the co-function identity and angle subtraction formula for cosine. Here's the solution:

cos(3π/2 - θ) = cos(3π/2)cos(θ) + sin(3π/2)sin(θ)

Since cos(3π/2) = 0 and sin(3π/2) = -1, the equation becomes:

cos(3π/2 - θ) = 0*cos(θ) + (-1)*sin(θ)

cos(3π/2 - θ) = -sin(θ)

Thus, the identity cos(3π/2 - θ) = -sin(θ) is established.

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Answer:

6

Step-by-step explanation:

plug in x and y in to the equation

5(4)-2(7)

20-14=

6

Answer:

k = 9.34

Step-by-step explanation:

The number of Miles a car can be driven is proportional to the number of gallons of gasoline it uses.

x ∝ g

x = kg ....(1)

k is constant of proportionality, x is no of miles and g is no of gallons

The car can be driven 14 miles per one and a half gallon of gasoline used.

Here x = 14 and g = \(1\dfrac{1}{2}=\dfrac{3}{2}\)

Put values in equation (1) to find k.

\(k=\dfrac{14}{\dfrac{3}{2}}\\\\x=9.34\)

Hence, the value of constant of proportionality is 9.34.

A subset of a population selected to represent the population is a sample.

A sample is a subset of a population that is selected to represent the larger population as a whole. It is important to select a representative sample so that the results of the analysis are accurate and reliable.

A population can be defined as a group of individuals, objects, or subjects that share common observable characteristics or traits. A population is a group of things that share something in common, and it can be any size.

A sample is a smaller group of individuals, objects, or subjects that are taken from the population to perform research or statistical analysis. Samples are typically used in research to estimate what is happening in the population as a whole.

A subset is a subset of a larger group.

In other words, it is a smaller set that is part of a larger set. A subset can contain any number of elements or members, and it can be of any size.

Hence, the "a sample" is correct.

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Answer:

45 and 23

Step-by-step explanation:

Let x equal the first number and y equal the second number.

We can set the following equations up with our information:

\(x+y=68\)

\(x-y=22\)

Adding the two equations together, we get:

\(2x=90\)

Dividing by two, we receive \(x=45\)

We can plug this into our first equation to get \(45+y=68\).

Subtracting 45 from both sides, we get \(y=23\).

The two numbers are 45 and 23, solved using system of equations.

A system of equations is a set of equations, involving similar variables used to solve for the variables simultaneously.

In the question, we are asked to find the two numbers, whose sum is 68 and the difference is 22.

We assume the two numbers to be x and y.

The sum of the two numbers is given to be 68.

This can be shown as an equation, x + y = 68 ... (i).

The difference of the two numbers is given to be 22.

This can be shown as an equation, x - y = 22 ... (ii).

Equations (i) and (ii) together makes a system of equation in the variables x and y.

To solve for the system of equation, we add (i) and (ii), to get:

x + y = 68

x - y = 22

_________

2x  = 90,

or, x = 45.

Substituting x = 45 in (i), we get:

x + y = 68,

or, 45 + y = 68,

or, y = 23.

Thus, the two numbers are 45 and 23, solved using system of equations.

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What is covariance

Covariance measures the directional relationship between the returns of two assets. A positive covariance means that the asset returns move together, a negative covariance means they move in opposite directions.

What does covariance between two variables mean?

Covariance measures the direction of the relationship between two variables. A positive covariance means that both variables tend to be high or low at the same time. Negative covariance means that as one variable increases, the other tends to decrease.

correlation coefficient

Correlation coefficient measures the strength of association between two variables. The most common correlation coefficient, called the Pearson product-moment correlation coefficient, measures the strength of linear association between variables measured on an interval or ratio scale.

according to the question given data,

the greater the absolute size of the correlation coefficient, the greater is the covariation between the two variables ,or the stronger is their relationship,(true)

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The probability she makes at least 65 is 0.0139.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

\(\begin{aligned}P(x \geq 65) & =1-P(x < 65) \\& =1-P\left(\frac{x-\mu}{n} < \frac{65-56}{4.0988}\right) \\& =1-P(z < 2.1958) \\& =1-0.9861 \\& =0.0139\end{aligned}\)

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The expression can be simplified as follows:

a. (-4)(-2) -6(2 - 5) = 26

b. 12.7 - 18.5 + 15 + 6.3 - 1 + 28.5 = 43

c. 23 - (17 - 3.4)² +  6 = -155.96

The expressions can be solved using PEMDAS rule,

P = Parenthesis

E = Exponential

M = Multiplication

D = division

A = addition

S = Subtraction

Hence,

a.

(-4)(-2) -6(2 - 5) = (-4)(-2) - 6(-3) = 8 + 18 = 26

b.

12.7 - 18.5 + 15 + 6.3 - 1 + 28.5 = -5.8 + 15 + 6.3 - 1 + 28.5 = 9.2 + 6.3 - 1 + 28.5 = 15.5 - 1 + 28.5 = 14.5 + 28.5 = 43

c.

23 - (17 - 3.4)² +  6 = 23 - (13.6)² + 6 = 23 - 184.96 + 6 = -161.96 + 6 = -155.96

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Answer:

\(\frac{27y^6}{8x^{12}}\)

Step-by-step explanation:

1) Use Product Rule: \(x^ax^b=x^{a+b}\).

\((\frac{3x^{-5+2}{y^3}}{2z^0yx}) ^3\)

2) Use Negative Power Rule: \(x^{-a}=\frac{1}{x^a}\).

\((\frac{3\times\frac{1}{x^3} y^3}{2x^0yx} )^3\)

3) Use Rule of Zero: \(x^0=1\).

\((\frac{\frac{3y^3}{x^3} }{2\times1\times yx} )^3\)

4) use Product Rule: \(x^ax^b=x^{a+b}\).

\((\frac{3y^3}{2x^{3+1}y} )^3\)

5) Use Quotient Rule: \(\frac{x^a}{x^b} =x^{a-b}\).

\((\frac{3y^{3-1}x^{-4}}{2} )^3\)

6) Use Negative Power Rule: \(x^{-a}=\frac{1}{x^a}\).

\((\frac{3y^2\times\frac{1}{x^4} }{2} )^3\)

7) Use Division Distributive Property: \((\frac{x}{y} )^a=\frac{x^a}{y^a}\).

\(\frac{(3y^2)^3}{2x^4}\)

8) Use Multiplication Distributive Property:  \((xy)^a=x^ay^a\).

\(\frac{(3^3(y^2)^3}{(2x^4)^3}\)

9) Use Power Rule: \((x^a)^b=x^{ab}\).

\(\frac{27y^6}{(2x^4)^3}\)

10)  Use Multiplication Distributive Property:  \((xy)^a=x^ay^a\).

\(\frac{26y^6}{(2^3)(x^4)^3}\)

11) Use Power Rule: \((x^a)^b=x^{ab}\).

\(\frac{27y^6}{8x^12}\)

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Answer:

\(\displaystyle \frac{27y^{6}}{8x^{12}}\)

Step-by-step explanation:

\(\displaystyle \biggr(\frac{3x^{-5}y^3x^2}{2z^0yx}\biggr)^3\\\\=\biggr(\frac{3x^{-5}y^2x}{2}\biggr)^3\\\\=\frac{(3x^{-5}y^2x)^3}{2^3}\\\\=\frac{3^3x^{-5*3}y^{2*3}x^3}{8}\\\\=\frac{27x^{-15}y^{6}x^3}{8}\\\\=\frac{27y^{6}x^3}{8x^{15}}\\\\=\frac{27y^{6}}{8x^{12}}\)

Notes:

1) Make sure when raising a variable with an exponent to an exponent that the exponents get multiplied

2) Variables with negative exponents in the numerator become positive and go in the denominator (like with \(x^{-15}\))

3) When raising a fraction to an exponent, it applies to BOTH the numerator and denominator

Hope this helped!

We have 792 ways to pick five students for the student council from a group of twelve candidates.

We will use the combination formula, which is nCr = n! / r!(n - r)! is find  number of ways to pick five students.

In this case, we want to choose 5 students from 12 candidates:

12C5 = 12! / 5!(12 - 5)!

12C5 = (12 × 11 × 10 × 9 × 8) / (5 × 4 × 3 × 2 × 1)

12C5 = 95040 / 120

12C5 = 792

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Albert) Let's define

Then,

To calculate A, we have the following compound interest formula:

L is easy to calculate:

To calculate B, we have a formula as well:

Then,

The balance of Albert's $2000 after ten years is $2159.07.

Answer:

Which table?????????????

Therefore , the solution of the given problem of percentage comes out to be 32 liters after 60% increased.

Any value that may be expressed as a fraction of 100 is referred to as a percentage in mathematics. The acronyms "pct.," "pct," or "pc" are also occasionally used. However, the "%" symbol is typically used to denote it. The proportional amount has no dimensions and is flat. Percentages can be viewed as fractions because their numerator is 100. To indicate that a number is a percent, it needs to be followed by the percent symbol (%).

Here,

Given:

=> 20 liters is the given volume

It is increased by 60% ,

then the final volume is :

=> 20 + 60/100 *20

=> 20 + 0.6*20

=> 20 + 12

=> 32 liters

Therefore , the solution of the given problem of percentage comes out to be 32 liters after 60% increased.

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The pattern using the rule n x 4, starting at 9 is 9, 36, 72, 108, 144, 180, 216, 252, 288, 324

To create this pattern, we start with the number 9 and then apply the rule n x 4 to each subsequent number. This means that we multiply each number by 4 to get the next number in the pattern. So:

9 x 4 = 36

36 x 4 = 72

72 x 4 = 108

108 x 4 = 144

144 x 4 = 180

180 x 4 = 216

216 x 4 = 252

252 x 4 = 288

288 x 4 = 324

And so on, if we wanted to continue the pattern.

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Answer:

1500 meters.

Step-by-step explanation:

Answer:

1500 meters

hope this helps youu

Answer:

1. \(p \leq 10\) where \(p\) represents the total number of people.

2. \(p \geq 8\) where \(p\) represents the total number of people.

3. \(c \leq 60\) where \(c\) represents the cost of a pair of jeans.

4. \(p > 20\) where \(p\) represents the total number of people.

Step-by-step explanation:

Question 1 explanation: Since no more than 10 people are allowed in the elevator, that means 10 and under are allowed, so the inequality would be \(p \leq 10\).

Question 2 explanation: Since the tour bus needs at least 8 people to sign up to run, that means 8 and more people will allow the tour bus to run, so the inequality would be \(p \geq 8\)

Question 3 explanation: Since the most you will pay for a pair of jeans is $60, that means jeans costing $60 and under are fine, so the inequality would be \(c \leq 60\).

Question 4 explanation: Since over 20 people showed up to the party, that means there were more than 20 people at the party, so the inequality would be \(p > 20\).

Answer:

x = 168

Step-by-step explanation:

A hexagon's total interior angles sums up to be 720, so what you have to do is just subtract.

x = 720-(84+128+150+103+87)

x = 168

The value of a that satisfies the given conditions is  (a) 2.

To find the value of a, we can use the given information that the volume of the region bounded above by z = a² - x² - y² and below by the xy-plane, and lying outside x² + y² = 1, is 32π units³. By comparing this equation with the equation of a cone, we can see that the region represents a cone with a height of a and a radius of 1.

The volume of a cone is given by V = (1/3)πr²h, where r is the radius and h is the height. Comparing this formula with the given volume of 32π units³, we can equate the two expressions and solve for a. By substituting the values, we get 32π = (1/3)π(1²)(a). Simplifying the equation, we find that a = 3.

Therefore, the value of a that satisfies the given conditions is (a) 2.

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Answer:

Step-by-step explanation: I got 14.4 but I might be wrong and im sorry if I am

(a) For a upper-tailed F test with v1 = 5 and v2 = 10, and an observed F value of 4.75, the p-value represents the probability of observing an F value as extreme or more extreme than 4.75 under the null hypothesis.

To find the p-value, we would compare the observed F value to the critical F value corresponding to the desired significance level (alpha) and degrees of freedom. Without the critical F value or the alpha level, we cannot determine the exact p-value.

(b) Similarly, for an upper-tailed F test with v1 = 5 and v2 = 10, and an observed F value of 2.00, we would need the critical F value or the alpha level to determine the p-value. The p-value represents the probability of observing an F value as extreme or more extreme than 2.00.

(c) In a two-tailed F test with v1 = 5 and v2 = 10, and an observed F value of 5.64, we can find the p-value by comparing the observed F value to the critical F value(s) corresponding to the desired significance level (alpha) and degrees of freedom. The p-value represents the probability of observing an F value as extreme or more extreme than 5.64 in either tail of the F distribution.

(d) For a lower-tailed F test with v1 = 5 and v2 = 10, and an observed F value of 0.200, we would need the critical F value or the alpha level to determine the p-value. The p-value represents the probability of observing an F value as extreme or more extreme than 0.200 in the lower tail of the F distribution.

(e) In an upper-tailed F test with v1 = 35 and v2 = 20, and an observed F value of 3.24, we would need the critical F value or the alpha level to determine the p-value. The p-value represents the probability of observing an F value as extreme or more extreme than 3.24. To calculate the exact p-value for each situation, we need the critical F value or the alpha level associated with the specific degrees of freedom. Without that information, we cannot provide the precise p-values.

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The probability that a randomly chosen sophomore is taking Algebra 2, given that they do not take Chemistry, is 19/36.

To find the probability that a randomly chosen sophomore is taking Algebra 2, given that they are not taking Chemistry, we need to consider the number of students taking Algebra 2 who are not taking Chemistry.

Given that there are 318 sophomores in total, and 102 are taking Chemistry, it means that 318 - 102 = 216 sophomores are not taking Chemistry.

Out of the 140 sophomores taking Algebra 2, 26 are also taking Chemistry. Therefore, the number of sophomores taking Algebra 2 but not taking Chemistry is 140 - 26 = 114.

Since we are considering only the students who are not taking Chemistry, the total number of students in this group is 216.

The probability of a randomly chosen sophomore being in this group (taking Algebra 2 but not taking Chemistry) is given by:

Probability = Number of favorable outcomes / Total number of outcomes

Probability = 114 / 216

Simplifying the fraction, we get:

Probability = 19 / 36

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