a faulty watch gains 10 seconds an hour if it is correctly set to 8 p.m. one evening what time will it show when the correct time is 8 p.m. the following evening​

To find the average rate of change of a function, we must first calculate the slope between two points.

To calculate the slope, we will use the formula m = (y2 - y1) / (x2 - x1). For the given points, we must first substitute the given values into the formula to get:

m = (f(x) - f(x)) / (x - x)
m = (0 - 0) / (x - x)
m = 0

Therefore, the average rate of change of the function f(x) as x changes from x to x is 0.

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Given that a restaurant has a total of 16 tables, each of which can seat a maximum of 4 people, and if 50 people were sitting at the tables in the restaurant with no tables empty, we need to find out the greatest possible number of tables that could be occupied by just 1 person.

Here, the maximum number of people that can be seated in the restaurant = 16 tables × 4 persons per table = 64 persons.Thus, number of empty seats = 64 − 50 = 14 empty seats.Let's assume x be the greatest possible number of tables that could be occupied by just 1 person. So, number of tables occupied by more than one person = 16 − x.

As the 50 people are seated in the restaurant, the number of persons occupying more than one seat plus the number of persons occupying exactly one seat should add up to 50. So, the number of persons occupying more than one seat = 50 − number of persons occupying exactly one seat = 50 − x.So, the total number of seats occupied is:x + 2(16 − x) = 50 − x⇒ 3x = 18⇒ x = 6.Hence, the greatest possible number of tables that could be occupied by just 1 person is 6.

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A percentile tells you what percentage of a distribution scored below a specific score and hence, option C) is the correct answer.

A percentile is a measure used to indicate the value below which a given percentage of observations in a group of observations falls. For a set of data, a percentile is the number below which a certain percentage of data fall.

In other words, a percentile is the percentage of observations that fall below a particular score in a distribution. The percentile rank of a score represents the percentage of people who have lower scores.

When it comes to percentile scores, there is a range of scores that are associated with a percentile rank, and each score in that range corresponds to the same percentile rank.

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Rebecca needs 6 \( \frac{1}{4} \) more yards of fabric to make the quilt.

Firstly calculating the fabric available to Rebecca = 2 \( \frac{1}{2} \) + 4 \( \frac{1}{4} \)

Fabric available to Rebecca = 5/2 + 17/4

Taking LCM we get 4

Fabric available to Rebecca = 10 + 17/4

Fabric available to Rebecca = 27/4

Let the required fabric be x. So,

17/4 + x = 21/2

x = 21/2 - 17/4

Performing subtraction

Taking LCM we get 4

x = 42 - 17/4

x = 25/4

Converting it back into mixed fraction -

x = 6 \( \frac{1}{4} \)

Thus, the required fabric is 6 \( \frac{1}{4} \) yards.

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The complete question is -

Rebecca needs 10 1/2 yards of fabric to make a quilt. She has one piece of fabric that is 2 1/2 yards and another piece of fabric that is 4 1/4 yards. How many more yards of fabric does Rebecca need to make a quilt.

Substituting the value of \( r \), we get \( V \approx 1105.4 \) mm³. Finally, dividing the mass of the ball-bearing (11.9 g) by its volume (1105.4 mm³) and converting the units, we can determine the density in g/cm³. The density is approximately 0.0108 g/cm³.

To explain the process in more detail, we start by finding the radius of the ball-bearing using the circumference formula. The circumference is given as 43.4 mm, so dividing it by 2π gives us the radius of approximately 6.912 mm.

Next, we calculate the volume of the sphere using the formula \( V = \frac{4}{3}\pi r^3 \). Plugging in the radius value, we obtain the volume of the metal ball-bearing as approximately 1105.4 mm³.

To calculate the density, we divide the mass of the ball-bearing (11.9 g) by its volume (1105.4 mm³). However, to obtain the density in g/cm³, we need to convert the volume from mm³ to cm³ by dividing it by 1000. After performing the division and conversion, we find the density of the metal ball-bearing to be approximately 0.0108 g/cm³.

Density is a fundamental property of matter that describes how much mass is contained within a given volume. In this case, it allows us to understand the mass-to-volume ratio of the metal ball-bearing. By calculating the density, we can characterize the compactness or heaviness of the material.

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The density of the metal in the ball-bearing is approximately 10.981 g/cm^3.

To find the density of the metal in g/cm^3, we need to calculate the volume of the metal ball-bearing and divide it by its mass.

Given information:

Circumference of the ball-bearing = 43.4 mm

Weight of the ball-bearing = 11.9 g

To calculate the volume of the ball-bearing, we need to find its radius (r). We can use the formula for the circumference of a circle:

Circumference = 2πr

Substituting the given circumference

43.4 mm = 2πr

To find the radius, divide both sides by 2π:

r = 43.4 mm / (2π) ≈ 6.9134 mm

Next, let's convert the radius to centimeters:

r = 6.9134 mm / 10 ≈ 0.69134 cm

Now we can calculate the volume of the ball-bearing using the formula for the volume of a sphere:

V = (4/3)πr^3

Substituting the radius:

V = (4/3)π(0.69134 cm)^3

Calculating this expression:

V ≈ 1.083 cm^3

Finally, to find the density, we divide the mass by the volume:

Density = Mass / Volume

Density = 11.9 g / 1.083 cm^3

Calculating this expression:

Density ≈ 10.981 g/cm^3

Therefore, the density of the metal in the ball-bearing is approximately 10.981 g/cm^3.

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The relation 2 represents a function.

In order to determine which relation in the below table represents a function, we need to first understand what a function is.A function is a relationship in which each input value corresponds to exactly one output value.

To put it another way, each x-value has one and only one y-value. The most typical method to determine whether a relation is a function is to use the vertical line test.

The vertical line test is a way to determine if a relation is a function graphically. To test if a graph is a function, we draw a vertical line through each x-value on the graph. If a vertical line crosses the graph more than once, it is not a function.

If, on the other hand, the graph passes the vertical line test and no vertical line crosses the graph more than once, it is a function.Now let's look at the table below to determine which relation is a function.

We will first plot the x and y values of each relation on a coordinate system and then apply the vertical line test to each relation.

Relation 1: x | y0 | 10 | 11 | 22 | 23 | 34 | 35 | 4Relation 1 does not represent a function since we can draw a vertical line through x = 3 and the line will cross the graph more than once.

Relation 2: x | y2 | 33 | 34 | 45 | 46 | 57 | 5Relation 2 represents a function since we can draw a vertical line through each x-value on the graph and it will only cross the graph once.

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Ce clasă ești sa văd daca te pot ajuta

Answer:

third option

Step-by-step explanation:

There is a common difference d between consecutive terms in the sequence, that is

d = - 13 - (- 10) = - 16 - (- 13) = - 3

This indicates the sequence is arithmetic with n th term

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 10 and d = - 3, then

\(a_{n}\) = - 10 - 3(n - 1) = - 10 - 3n + 3 = - 7 - 3n

Thus the sum of the first 6 terms is represented by

∑ - 7 - 3n ( for n = 1 to 6 )

The 95% confidence interval for p is 0.26 ± 2.63 * sqrt((0.26 * (1 - 0.26)) / 300). The correct answer is option b.

For the first problem:

The question asks whether a sample size of n = 108 is large enough to use an inferential procedure. The correct answer is: O Yes, since both n and np (where p is the proportion of interest) are greater than or equal to 15.

To determine if a sample size is large enough to use an inferential procedure for proportions, both the sample size (n) and the product of the sample size and the proportion of interest (np) should be greater than or equal to 15. In this case, n = 108, and since the proportion is not provided, we cannot verify whether np is greater than or equal to 15. Therefore, we cannot determine if the sample size is large enough based on the information given.

For the second problem:

To find the 95% confidence interval for p (proportion), we can use the formula:

p ± z * sqrt((p * (1 - p)) / n)

p = 0.26 (probability of success)

n = 300 (sample size)

z = 1.96 (z-value for a 95% confidence level)

Using the formula, the 95% confidence interval for p is:

0.26 ± 1.96 * sqrt((0.26 * (1 - 0.26)) / 300)

Therefore, the correct answer is option b.

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Answer:

\(4\) x \(10^{6}\)

Step-by-step explanation:

Answer:

4*10^6

Step-by-step explanation:

Answer:

The x-intercept occurs when y is zero. The y-intercept is the point, (0,b) , where the graph crosses the y-axis . The y-intercept occurs when x is zero.

Step-by-step explanation:

The explicit formula for f^-1 is (x-3)^(1/4) and this is obtained by switching the roles of x and y and solving for y in terms of x.

To find the inverse function of f(x)=x^4+3, we need to switch the roles of x and y, and solve for y.
Let y = x^4+3
Subtract 3 from both sides to get:
y - 3 = x^4
Take the fourth root of both sides to isolate x:
(x^4)^(1/4) = (y-3)^(1/4)
Simplify:
x = (y-3)^(1/4)
So the inverse function of f(x) is:
f^-1 (x) = (x-3)^(1/4)
This is the explicit formula for the inverse function of f(x).
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The answer is A. The function g(x) = x is a unit vector in the vector space C[0, 1] and B. The cosine of the angle between \(f(x) = 5x^2\) and g(x) = 9x is 15 /\((2\sqrt{15})\).

To determine whether the function f(x) = 3x is a unit vector in the vector space C[0, 1] with the given inner product, we need to calculate its norm or magnitude.

The norm of a function f(x) in this vector space is defined as ||f|| = sqrt((f, f)), where (f, f) is the inner product of f with itself.

Using the inner product given, we can calculate the norm of f(x) as follows:

\(||f|| = sqrt(integral^1_0 (3x)^2 dx)\\= sqrt(integral^1_0 9x^2 dx)\\= sqrt[9 * (x^3/3) | from 0 to 1]\)

= sqrt[9/3 - 0]

= sqrt(3).

Since the norm of f(x) is sqrt(3) ≠ 1, we can conclude that f(x) = 3x is not a unit vector in this vector space.

To find a function that is a unit vector, we need to normalize f(x) by dividing it by its norm. Let's denote this normalized function as g(x):

g(x) = f(x) / ||f||

= (3x) / sqrt(3)

= sqrt(3)x / sqrt(3)

= x.

Therefore, the function g(x) = x is a unit vector in the vector space C[0, 1].

(b) To find the cosine of the angle between \(f(x) = 5x^2\) and g(x) = 9x, we can use the inner product and the definition of cosine:

cos(θ) = (f, g) / (||f|| ||g||).

Using the given inner product, we have:

\((f, g) = integral^1_0 (5x^2)(9x) \\\\dx= 45 * integral^1_0 x^3 \\\\dx= 45 * (x^4/4 | from 0 to 1)\)

= 45/4.

The norms of f(x) and g(x) are:

\(||f|| = sqrt(integral^1_0 (5x^2)^2 dx)\\= sqrt(integral^1_0 25x^4 dx)\\= sqrt[25 * (x^5/5) | from 0 to 1]\)

= sqrt(5).

\(= sqrt(integral^1_0 81x^2 dx)\)

\(= sqrt(integral^1_0 81x^2 dx)\)

\(= sqrt[81 * (x^3/3) | from 0 to 1]\)

\(= 3\sqrt{3}\)

Substituting these values into the cosine formula:

cos(θ) = (45/4) / (sqrt(5) * 3√3)

\(= (15/2) * (1 / (sqrt(5) * √3))= (15/2) * (1 / √15)= (15/2) * (1 / (√3 * √5))= 15 / (2√15).\)

Therefore, the cosine of the angle between \(f(x) = 5x^2 and g(x) = 9x is 15 / (2\sqrt{15}).\)

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Answer: 121 im pretty sure

Step-by-step explanation: 21175 divided by 175

Answer:

\((x+1)(x-1)(x-2)\)

Step-by-step explanation:

\(x^3-2x^2-x+2\)

Look at this as 2 separate expressions for now, being the first 2 terms and the last 2 terms:

\(\mbox{1. }x^3-2x^2\\\mbox{2. }-x+2\)

Factor both of these individually, starting with the first one. The greatest common factor here is x², so factor that out:

\(\rightarrow x^3-2x^2\\\rightarrow x^2(x-2)\)

Now the second equation. There isn't really a GCF here, but you still should factor out a -1 to get the x on its own.

\(\rightarrow -x+2\\\rightarrow -1(x-2)\)

Together, that leaves you with this:

\(x^2(x-2)-1(x-2)\)

This is actually another expression that can be factored. The GCF here is (x - 2):

\(\rightarrow x^2(x-2)-1(x-2)\\\rightarrow (x^2-1)(x-2)\)

Finally, you can expand that (x² - 1) further using this rule:

\((x^2-y^2)=(x+y)(x-y)\)

1 is equal to 1², so you can rewrite that term and then expand it with the rule above:

\(\rightarrow (x^2-1^2)(x-2)\\\rightarrow (x+1)(x-1)(x-2)\)

\( {x}^{3} - {2x}^{2} - x + 2 \\ = {x}^{2} (x - 2) - 1(x - 2) \\ = ( {x}^{2} - 1)(x - 2) \\ = ( {(x)}^{2} - {(1)}^{2} )(x - 2) \\ = (x + 1)(x - 1)(x - 2)\)

Answer:

(x + 1)(x - 1)(x - 2)

Hope you could understand.

If you have any query, feel free to ask.

Answer:

x=4

Step-by-step explanation:

4(3+2x)+2=46

12+8x+2=46

12+8x=44

8x=32

x=4

Answer:

4

Step-by-step explanation:

You need to start with the 2x inside the parenthesis

If you put 4 in place of x you get 8

8+3=11

then because there isnt any sign between 4 and the parenthesis you multiply

4x11=44

then its easy

44+2=46

The amount that needs to be invested at the interest rate of 4% compounded continuously is P = $8932.461.

Compound interest, also known as interest on principal and interest, is the practise of adding interest to the principal amount of a loan or deposit. It occurs when interest is reinvested, or added to the loaned capital rather than paid out, or when the borrower is required to pay it, so that interest is generated the next period on the principal amount plus any accumulated interest. In finance and economics, compound interest is common.

Given that the interest is compounded continuously.

For the given situation the formula of compound interest is:

\(A = Pe^{rt}\)

where, A is the amount = $12300

P is the principal amount

r is the rate = 4% = 0.04

t is the time = 8 years

Substituting the values we have:

\(12300 = Pe^{(0.04)(8)}\\\\P = \frac{12300}{e^{(0.04)(8)}} \\\\P =8932.461\)

Hence, the amount that needs to be invested at the interest rate of 4% compounded continuously is P = $8932.461.

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Answer:

10.6 hours

Step-by-step explanation:

Answer: look at the picture

Step-by-step explanation: Hope this help

Answer:

x=-4

Step-by-step explanation:

4x+16/5=4-x

4x+16=-20-5x

4x+5x=-20-16

9x=-36

x=-4

Answer:

\(x = 36\)

Step-by-step explanation:

\( \frac{4(x + 4)}{5} = - 4 - x \\ \frac{4x + 16}{5} = - 4 - x \\ 4x + 16 = - 20 - 5x \\ - x = - 36 \\ x = 36\)

Answer:

2/5 is already a fraction.... it's an improper fraction.

Answer:

1) 20.864

2) 195.4

3) 17.6

4) 38.05

5) 1.76

6) 6.11

Step-by-step explanation:

(8.15 × 4 ÷ 5) × 3.2

= (32.6 ÷ 5) × 3.2

= 6.52 × 3.2

= 20.864

125 + 32 × 2.2

= 125 + 70.4

= 195.4

17 + 8 × (2.7 ÷ 6) - 3

= 17 + 8 × 0.45 - 3

= 17 + 3.6 - 3

= 17 + 0.6

= 17.6

38.9 - 2.3 × 1.5 + 2.6

= 38.9 - 3.45 + 2.6

= 38.9 - 0.85

= 38.05

0.2 × (5 - 0.7) + 1.8 ÷ 2

= 0.2 × 4.3 + 0.9

= 0.86 + 0.9

= 1.76

21.5 ÷ 5 + (8.06 - 12.5 ÷ 2)

= 4.3 + (8.06 - 6.25)

= 4.3 + 1.81

= 6.11

The correct values in the first column, under the true mean of 10.5, can be determined through a series of calculations

To calculate the values, we need to consider the concept of sampling distribution. The distribution of sample means follows a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

Assume we have a sample size of n = 100, and the population standard deviation is known to be 2.5. Using these values, we can calculate the standard error (SE) as follows:

SE = population standard deviation / √(sample size)

= 2.5 / √(100)

= 2.5 / 10

= 0.25

Next, we can calculate the values in the first column by adding and subtracting the margin of error from the true mean:

True Mean ± Margin of Error

For a 95% confidence interval, the margin of error can be calculated using the formula:

Margin of Error = Critical Value * Standard Error

The critical value for a 95% confidence interval is approximately 1.96. Therefore, the margin of error is:

Margin of Error = 1.96 * 0.25

= 0.49

Now, let's calculate the values in the first column:

True Mean + Margin of Error

= 10.5 + 0.49

= 10.99

True Mean - Margin of Error

= 10.5 - 0.49

= 10.01

Therefore, the correct values in the first column (under the true mean of 10.5) are: 10.01 and 10.99.

To calculate the values, we used the concept of sampling distribution. We determined the standard error (SE) by dividing the population standard deviation by the square root of the sample size. With a sample size of 100 and a population standard deviation of 2.5, the SE was calculated as 0.25. The margin of error was then obtained by multiplying the critical value (1.96 for a 95% confidence interval) by the SE. Finally, by adding and subtracting the margin of error from the true mean of 10.5, we obtained the values of 10.01 and 10.99.

The correct values in the first column, representing a 95% confidence interval around the true mean of 10.5, are 10.01 and 10.99.

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Answer: To find the product of the four given expressions, you can use the distributive property to expand each expression and then multiply the terms.

(2x + 1)(x + 2) = (2x + 1)(x) + (2x + 1)(2) = 2x^2 + 2x + x + 2 = 3x^2 + 3x + 2

(2x + 3y)(x + y) = (2x + 3y)(x) + (2x + 3y)(y) = 2x^2 + 3xy + 2xy + 3y^2 = 2x^2 + 5xy + 3y^2

(x + 3y)(2x + y) = (x + 3y)(2x) + (x + 3y)(y) = 2x^2 + 3xy + xy + 3y^2 = 3x^2 + 4xy + 3y^2

(2x+3)(x - 1) = (2x+3)(x) + (2x+3)(-1) = 2x^2 + 3x - 2x - 3 = 2x^2 - x - 3

So the product of the four given expressions is 3x^2 + 3x + 2, 2x^2 + 5xy + 3y^2, 3x^2 + 4xy + 3y^2, and 2x^2 - x - 3.

Using a system of equations, it is found that:

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, the variables are given as follows:

The total invested is of $36,000, hence:

x + y = 36000.

The amount invested in bonds is to to exceed that in CDs by $5,000, hence:

x = y + 5000.

Replacing in the first equation:

y + 5000 + y = 36000.

2y = 31000

y = 15,500.

x = y + 5000 = 20,500.

Hence:

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Answer:

Keep it simple. C is the answer

Step-by-step explanation:

Answer:

C) His solution for x is correct, but in order for 6 to be an extraneous solution, one denominator has to result in 0 when 6 is substituted for x.

The student's solution is that C. the solution for x is correct, but in order for 6 to be an extraneous solution, one denominator has to result in 0.

It should be noted that an extraneous solution simply means the root of a transformed equation that isn't a root of the original equation.

In this case, the solution for x is correct, but in order for 6 to be an extraneous solution, one denominator has to result in 0 when 6 is substituted for x.

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Answer:

6:7

Step-by-step explanation:

1.5 m=150 cm

ratio of their hight is 150/175=30/35=6/7

=6:7

The proportion equation is A = 6 : 7

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the proportion equation be represented as A

Now , the value of A is

The height of Maisa is P = 1.5 m

The value of 1.5 m = 150 cm

And , the height of Arman = 175 cm

So , the proportion is

A = height of Maisa / height of Arman

Substituting the values in the equation , we get

A = 150 / 175

A = 6/7

Therefore , the value of  A is 6 : 7

Hence , the proportion is 6 : 7

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