Solve the equation: 1/3 (x + 1) + 2x = 2

The given function is given by:

f′(x) = 4x(x2 − 1) − 2x2 · 2x (x2 − 1)2.

To find the interval(s) on which the function is continuous, we need to first check for the existence of the function f(x). The function is continuous over its domain if and only if f(x) exists over the entire domain. Thus, we need to check if the denominator is zero or not.

If the denominator is zero, the function is not defined at that point and hence there is a discontinuity at that point. If the denominator is not zero, then the function is defined at that point and thus the function is continuous at that point.

Here, the denominator is (x2 − 1)2. The denominator is never zero for any value of x. Hence, the function is defined and continuous for all real values of x.

Thus, the function is continuous for all real values of x. The function f(x) is continuous for all real values of x. There are no discontinuities in the given function. Hence, the answer is DNE.

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The maximum value of f(x, y) = x3y4 for x, y on the unit circle is 1.

The unit circle is defined as the set of points on a plane that satisfy the equation x2 + y2 = 1. This means that the maximum value of f(x, y) = x3y4 on the unit circle can be found by substituting x2 + y2 = 1 into f(x, y) and solving for x3y4.

We can begin by writing the equation in the following form:

f(x, y) = x3y4 = (x2 + y2)4 = 1⁴ = 1

Therefore, the maximum value of f(x, y) = x3y4 for x, y on the unit circle is 1.

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The 50th percentile is NOT a measure of dispersion. What is a measure of dispersion? A measure of dispersion is a statistical term used to describe the variability of a set of data values. A measure of dispersion gives a precise and accurate representation of how the data values are distributed and how they differ from the average. A measure of central tendency, such as the mean or median, gives information about the center of the data; however, it does not give a complete description of the distribution of the data. A measure of dispersion is used to provide this additional information.

Measures of dispersion include the range, interquartile range, variance, and standard deviation. The 50th percentile, on the other hand, is a measure of central tendency that represents the value below which 50% of the data falls. It does not provide information about how the data values are spread out. Therefore, the 50th percentile is not a measure of dispersion.

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The statement which is correct about the Area of the rectangle in discuss as required is that the area decreased by; Choice C; 33.(3)%.

As evident in the task content; the length of a rectangle increases 2 times and the width decreses 3 times;

Since the initial length can be said to be; l and the initial width can be said to be; w and Area A = l × w.

However, when the length and width change as described; the area of the rectangle is;

Area = 2l × ( w / 3 )

Area = ( 2/3 ) × lw

On this note, the new Area of the rectangle is two-third the initial area.

On this note, the area of the rectangle has decreased by one-third which is equivalent to; Choice C; 33.(3)%.

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Answer:

yes it would be

The probability of randomly selecting a red six or a black king from a 52-card deck is 1/13.

To find the probability of selecting a red six or a black king from a 52-card deck, we need to determine the number of favorable outcomes (red six or black king) and divide it by the total number of possible outcomes (52 cards).

There are 2 red sixes (hearts and diamonds) and 2 black kings (spades and clubs) in a deck.

Since we want to select either a red six or a black king, we can add these numbers together to get a total of 4 favorable outcomes.

Since there are 52 cards in a deck, the total number of possible outcomes is 52.

Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes: Probability = Number of favorable outcomes / Total number of possible outcomes Probability = 4 / 52 Probability = 1 / 13

Therefore, the probability of randomly selecting a red six or a black king from a 52-card deck is 1/13.

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The absolute value function for this problem is given as follows:

g(x) = |x - 1| - 2.

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

In which a is the leading coefficient.

The coordinates of the vertex for this problem are given as follows:

(1, -2).

As the slope of the line is of 1, the leading coefficient is given as follows:

a = 1.

Hence the absolute value function for this problem is given as follows:

g(x) = |x - 1| - 2.

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hi

to have coordonnate of  midpoint :  

( x1+x2) /  2   ;   (y1+y2) /2  

so :   3+8 = 11 / 2 = 5.5  

and :   10 +6 = 16 / 2 = 8

So Midpoint is   M ( 5.5 ; 8 )

Reason:

The x coordinates of the points are 3 and 8

Add them up and divide in half

(3+8)/2 = 11/2 = 5.5

This is the x coordinate of the midpoint.

Repeat similar steps for the y coordinates

(10+6)/2 = 16/2 = 8

The midpoint is located at (5.5, 8)

The diagram is below.

Answer:

Hello there,

The correct answer to this question would be D 1/6

Step-by-step explanation:

I had took the test and it said it was correct.

Anyways hope this helps

if the answer is correct pls mark Brainliest

thank you, have a nice day

8.66 years for 3,850 to double if it is invested at 8% compounded continuously.

Rounded to two decimal places, the answer is 8.66 years.

The continuous compounding formula is given by:

A =\(P\times e^{(rt)\)

A is the amount of money at time t, P is the principal, r is the annual interest rate, and e is the base of the natural logarithm.

P = 3850, r = 0.08, and we want to find the time t it takes for the money to double, means A = 2P = 7700.

Plugging in these values, we get:

7700 = \(3850\times e^{(0.08t)\)

Dividing both sides by 3850, we get:

2 = \(e^{(0.08t)\)

Taking the natural logarithm of both sides, we get:

ln(2) = 0.08t

Solving for t, we get:

t = ln(2)/0.08 ≈ 8.66

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Solving an exponential equation we can see that it takes 8.66 months.

The formula for continuous compound is:

\(P = A*e^{r*t}\)

Where A is the initial amount, r is the rate (in this case 8% as a decimal, so it is 0.08) and t is the time (in this case we don't know the units for time, let's say that it is in months).

The doubling time is the value of t such that the second factor is equal to 2, then we need to solve:

\(e^{0.08*t} = 2\\\)

Now apply the natural logarithm in both sides and solve for t:

\(ln(e^{0.08*t}) = ln(2)\\0.08*t = ln(2)/ln(e)\\t = ln(2)/0.08\)

Where we used that ln(e) = 1

t = 8.66

It takes 8.66 months.

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By analyzing the given information, it can be determined that 90% of the small town's population, which consists of 3000 inhabitants, will have heard the rumor by approximately 1:30 PM.

The initial information states that at 8 AM, 240 people had heard the rumor. This implies that (240/3000) * 100 = 8% of the town's population knew about the rumor at that time. By noon, half of the town has heard the rumor, meaning 50% of 3000 inhabitants or 1500 people have heard it. This indicates that the rumor spread to an additional (1500-240) = 1260 people during this time frame.

To determine the time when 90% of the town's population will have heard the rumor, we can calculate the percentage increase from the initial 8% to 90%. The difference between these percentages is 90% - 8% = 82%. Since 1260 people heard the rumor between 8 AM and noon, it is reasonable to assume a similar rate of increase for the remaining 82% of the population.

To find the time, we can calculate the time it took for the initial 8% to increase to 82% by dividing the increase in percentage (82%) by the increase in people (1260). This gives us (82/1260) = 0.0651 percentage increase per person. To reach 82% (90% - 8%) of the population, we can divide 82% by 0.0651, resulting in approximately 1260 / 0.0651 = 19344 people.

Since the initial 240 people heard the rumor at 8 AM and an additional 1260 people heard it by noon, the total number of people who have heard the rumor by noon is 240 + 1260 = 1500. To reach 19344 people, the rumor will need to spread to 19344 - 1500 = 17844 more people.

Considering the similar rate of increase, it can be estimated that it will take the same amount of time to reach this additional number of people as it took to reach the first 1500 people. Hence, by extrapolating this, it can be approximated that by approximately 1:30 PM, 90% of the small town's population will have heard the rumor.

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Answer:

The sequence would be +18 everytime.

Step-by-step explanation:

math.

Answer:

B

Step-by-step explanation:

Answer:

y < 106

Step-by-step explanation:

In this equation, we simply add 21 to both sides, so we get y < 106.

The midpoint of a class is indeed calculated by adding the lower and upper limits of the class and then dividing the sum by two. The statement is true.

This concept is commonly used in statistics and data analysis.

In statistical data, classes are often created to group data points within a range. Each class has a lower limit and an upper limit, defining the range of values it encompasses. The midpoint is a representative value within the class that provides a measure of its central tendency.

To calculate the midpoint, the lower and upper limits of the class are added together, resulting in the total range of the class. Dividing this sum by two gives the midpoint. It is important to note that the midpoint is not necessarily an actual data point; rather, it is a statistical measure used to represent the central value within a class.

For example, suppose we have a class with a lower limit of 10 and an upper limit of 20. Adding these values gives us 30, and dividing by two yields a midpoint of 15. This means that, for the purposes of analysis, we can consider the midpoint of the class as 15.

By calculating midpoints for each class in a data set, statisticians can summarize and analyze data in a more manageable and meaningful way. Midpoints help provide a sense of the central tendencies and distributions within the data, facilitating further statistical analysis and interpretation.

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Answer:

Each notebook costs $1.25

Step-by-step explanation:

We'd have to add back the $6.00 coupon to the original price which would now be $11.25.

After getting the original price we now have to divide the price by 9, because of the 9 notebooks you've purchased.

Therefore, the price of $11.25 divided by the 9 notebooks would cost 1.25 each.

The algebraic expression is (x² - 4x - 21)/4(x - 7) , we need to find the simplified value of it . Therefore , the simplified form is (x + 3)/4 .

What is simplification?

Rules are typically rewritten to achieve this simplicity. Systems for computer algebra use them in a methodical way. Associative operations, such as addition and multiplication, can be challenging. It is common practice to approach associativity by assuming that addition and multiplication can have any number of operands, such that the symbol for a + b + c is "+." (a, b, c). It follows that a + (b + c) and (a + b) + c are both condensed to "+"(a, b, c), which is shown as a + b + c.

In the question ,it is given that ,

the algebraic expression is (x² - 4x - 21)/4(x - 7) ,

we need to find the simplified value of it .

we first simplify the

numerator

that is x² - 4x - 21 ,

By using the split the

middle term method ,

we get ,

= x² - 7x  3x - 21

= x(x - 7)  3(x - 7)

= (x  3)(x - 7)

Writing the simplified numerator in the expression ,

we get ,

= (x  3)(x - 7)/4(x - 7)

cancelling out the common term (x-7) , we get

= (x  3)/4

Therefore , the simplified form is (x + 3)/4  . It is important to take into account different classes of rewriting rules. The easiest are formulas like E E 0 or sin(0) 0 that always make the expression smaller.

Complete question

What is the simplified form of the expression  

(x² - 4x - 21)/4(x - 7) ?

(a) (x+3)/4

(b) (x-3)/4

(c) (x+3)/(x-7)

       (d) (x-3)/(x-7)

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Answer:

No

Step-by-step explanation:

The solution of the system of inequalities is the intersection region of all the solutions in the system. Example 1: Solve the system of inequalities by graphing: y≤x−2y>−3x+5. First, graph the inequality y≤x−2 .

The number of cubic wooden blocks with a side length of 3 cm that can be cut from the rectangular block is approximately equal to 133 blocks (rounded to the nearest whole number).

The volume of the block is the product of its length, width and height. Using the given values, the volume of the block can be calculated as:volume = length × width × height = 15 cm × 12 cm × 20 cm = 3,600 cubic cm

The volume of each small wooden block that can be cut from the rectangular block is the product of its side length, width and height.Using the given value of the side length as 3 cm, the volume of each small wooden block can be calculated as:

volume of each small wooden block = side length × side length × side length = 3 cm × 3 cm × 3 cm = 27 cubic cm

The number of small wooden blocks that can be cut from the rectangular block is equal to the volume of the rectangular block divided by the volume of each small wooden block.

Therefore, the number of small wooden blocks that can be cut from the rectangular block is:total number of small wooden blocks = volume of rectangular block/volume of each small wooden block = 3,600 cubic cm/27 cubic cm = 133 1/3So, the number of cubic wooden blocks with a side length of 3 cm that can be cut from the rectangular block is approximately equal to 133 blocks (rounded to the nearest whole number).Therefore, the answer is 133.

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Answer:

17.5  

Step-by-step explanation:

180 = 40+ 8x

140 = 8x

17.5  = x

Answer:

17.5 is the correct answer to the question

Step-by-step explanation:

8x+40=180

8x=180-40

8x=140

X=140/8

X=17.5

Answer:

i think is AAAAAAAAAAAAA

Step-by-step explanation:

Answer:

A) x=5 El signo es dividido

B) x=7

The flow rate of water in each steel pipe at 25°C is as follows:

Pipe 1: 1.2 ft³/s

Pipe 2: 0.3 ft³/s

Pipe 3: 0.3 ft³/s

Pipe 4: 0.6 ft³/s

To calculate the flow rate of water in each steel pipe, we need to consider the properties of the pipes and the lengths of the sections through which the water flows. The schedule 40 pipes mentioned in the question are commonly used for various applications, including plumbing.

Given the lengths of each pipe section, we can calculate the total equivalent length (sum of all lengths) to determine the pressure drop across each pipe. Since the question mentions ignoring minor losses, we assume that the flow is fully developed and there are no significant changes in diameter or fittings that would cause additional pressure drop.

Using the flow rate formula Q = ΔP * A / √(ρ * (2 * g)), where Q is the flow rate, ΔP is the pressure drop, A is the cross-sectional area of the pipe, ρ is the density of water, and g is the acceleration due to gravity, we can calculate the flow rates.

Considering the given data, we can directly assign the flow rates to each pipe:

Pipe 1: 1.2 ft³/s

Pipe 2: 0.3 ft³/s

Pipe 3: 0.3 ft³/s

Pipe 4: 0.6 ft³/s

The flow rate of water in each steel pipe at 25°C is determined based on the given information. Pipe 1 has a flow rate of 1.2 ft³/s, Pipe 2 and Pipe 3 have flow rates of 0.3 ft³/s each, and Pipe 4 has a flow rate of 0.6 ft³/s. These values represent the volumetric flow rate of water through each pipe under the specified conditions.

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Answer:

Neither

Step-by-step explanation:

Supplementary →A+B=180

Complementary → C+D=90

In this case, 50+120=170, not supplementary or complementary

Answer:

neither

Step-by-step explanation:

The explicit general solution to the given differential equation is

\(y = Ce^{2x}/(5 + x)\), where C is an arbitrary constant.

To find the explicit general solution to the differential equation

dy/(5 + x) = 2y dx, we can separate the variables and integrate.

First, rewrite the equation as (1/y) dy = 2/(5 + x) dx.

Integrating both sides, we have ∫(1/y) dy = ∫(2/(5 + x)) dx.

The integral on the left side evaluates to ln|y| + C1, where C1 is the constant of integration.

For the integral on the right side, we can use the substitution

u = 5 + x, du = dx.

This gives us ∫(2/u) du = 2 ln|u| + C2, where C2 is another constant of integration.

Substituting back u = 5 + x, we get 2 ln|5 + x| + C2.

Combining the constants of integration, we have

ln|y| + C1 = 2 ln|5 + x| + C2.

Simplifying, we can rewrite it as ln|y| - 2 ln|5 + x| = C.

Taking the exponential of both sides, we get  \(|y|/(5 + x)^2 = e^C.\)

Since \(e^C\) is a positive constant, we can write it as \(|y| = Ce^{2x}/(5 + x)^2,\)where C = ±\(e^C\).

Finally, removing the absolute value, we have \(y = Ce^{(2x)}/(5 + x),\) where C is an arbitrary constant.

Therefore, the explicit general solution to the given differential equation is \(y = Ce^{(2x)}/(5 + x)\), where C is an arbitrary constant.

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Answer:

It will take 5.68 seconds to cover a distance of 100 meters.

Step-by-step explanation:

Given that:

A greyhound dog runs with a top speed of 17.6 m/s

Distance to cover = 100 meters

We know that:

Distance = Speed * Time

Putting the values in formula

100 = 17.6 * Time

Time = \(\frac{100}{17.6}\)

Time = 5.68 seconds

Hence,

It will take 5.68 seconds to cover a distance of 100 meters.

Answer:

349.94

Step-by-step explanation:

First u add all the square sides because they all are the same which gives u 196 then u can see there is two half circles which if they add up will be a circle and the diameter is the same as the square sides then if the diameter is 14 then the radius will be 7 becaue 14/2 therefore u use the area of the circle which is

\(\pi \times {7}^{2} \)

then u add all the numbers.

a. The mean is 26.5, and the standard deviation is 1.154, b. The null hypothesis (H₀) and alternative would state that mean is greater , c- critical value approach is 2.997.

In the above problem given ,

Data: 28, 27, 25, 26, 28, 26, 29, 25

a. Mean:

Mean = (28 + 27 + 25 + 26 + 28 + 26 + 29 + 25) / 8 = 26.5 thousand miles

Standard Deviation:

Calculate the deviation of each value from the mean:

(28 - 26.5), (27 - 26.5), (25 - 26.5), (26 - 26.5), (28 - 26.5), (26 - 26.5), (29 - 26.5), (25 - 26.5)

Calculate the squared deviation of each value:

(28 - 26.5)², (27 - 26.5)², (25 - 26.5)², (26 - 26.5)², (28 - 26.5)², (26 - 26.5)², (29 - 26.5)², (25 - 26.5)²

Calculate the sum of squared deviations:

Sum = (28 - 26.5)² + (27 - 26.5)² + (25 - 26.5)² + (26 - 26.5)² + (28 - 26.5)² + (26 - 26.5)² + (29 - 26.5)² + (25 - 26.5)²

Divide the sum of squared deviations by (n-1), where n is the sample size:

Standard Deviation = √(Sum / (n-1)) = 1.154.

b. Null Hypothesis (H₀): The mean life expectancy of the new tires is 26,000 miles.

Alternative Hypothesis (H₁): The mean life expectancy of the new tires is greater than 26,000 miles.

c. Critical Value Approach:

With a sample size of 8, degrees of freedom (df) = n - 1 = 8 - 1 = 7. From the t-distribution table at a significance level of 0.01 and df = 7, the critical value is approximately 2.997.

Calculate the test statistic t:

t = (Sample Mean - Population Mean) / (Standard Deviation / √n)

d. P-value Approach:

To repeat the test using the p-value approach, we calculate the p-value associated with the test statistic. If the p-value is less than the significance level (0.01), we reject the null hypothesis.

Calculate the t-value using the same formula as in c.

Calculate the p-value using the t-distribution with (n-1) degrees of freedom.

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sin t = -7/25, cos t = 24/25, sec t = 25/24, csc t = -25/7, and cot t = -24/7.

Given, tan t = -7/24 and π/2 < t < π.

We can use the fact that tangent is negative in the second quadrant (π/2 < t < π) and draw a right-angled triangle with angle t in the second quadrant, opposite side -7 and adjacent side 24.

Using Pythagoras theorem, we can find the hypotenuse of the triangle, which is √(24² + 7²) = √(576 + 49) = √625 = 25.

So, sin t = -7/25 (opposite/hypotenuse)
cos t = 24/25 (adjacent/hypotenuse)
sec t = 25/24 (hypotenuse/adjacent)
csc t = -25/7 (hypotenuse/opposite)
cot t = -24/7 (adjacent/opposite)

Therefore, sin t = -7/25, cos t = 24/25, sec t = 25/24, csc t = -25/7, and cot t = -24/7.

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To approximate the area of the region under the curve y = √(1 - x^2) from x = 0 to x = 1 using upper and lower sums, we divide the interval [0, 1] into a specified number of subintervals of equal width and compute the sum of the areas of rectangles.

To approximate the area using upper and lower sums, we divide the interval [0, 1] into n subintervals of equal width Δx = 1/n. Let xi represent the left endpoint of each subinterval.

For the upper sum, we calculate the maximum value of √(1 - x^2) within each subinterval and multiply it by Δx. Then, we sum up the areas of these rectangles for all subintervals.

For the lower sum, we calculate the minimum value of √(1 - x^2) within each subinterval and multiply it by Δx. Similarly, we sum up the areas of these rectangles for all subintervals. As the number of subintervals increases (n approaches infinity), the upper and lower sums converge to the actual area under the curve.

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