please show all work and answers legibly
Problem 5. Find the limits of the sequences: sin(n2 + 1) + cos n (a) lim Inn (6) lim vn n- n2.7 -00

The points where the equation x²y + 3y³ = 24 has a horizontal tangent are (0, √8/3) and (0, -√8/3). Hence, the required answer is (0, √8/3), (0, -√8/3).

To find any point(s) where the equation\(x^2 y + 3y^3 = 24\) has a horizontal tangent, we need to differentiate the given equation partially and equate it to 0.

This will give us the value of x at which the tangent will be horizontal.

The given equation is x²y + 3y³ = 24.

To find the derivative with respect to x, we first differentiate both sides of the equation with respect to x by using the product rule of differentiation as shown below:

\($$\frac{d}{dx} (x^2y) + \frac{d}{dx} (3y^3) = \frac{d}{dx}(24)$$\)

Rearranging and simplifying, we obtain:

\($$y(2x + 9y^2) \frac{dy}{dx} = 0$$\)

This will give us 2 critical points for the derivative, i.e., (0,±√8/3). Now, we need to find the corresponding values of y for each of these critical points.

To find the corresponding values of y for (0, ±√8/3), we plug them into the original equation i.e., x²y + 3y³ = 24.

We have: y = √8/3 for x = 0 and y = -√8/3 for x = 0.

Substituting these values in the original equation, we get the following points:

(0, √8/3) and (0, -√8/3).

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Answer:

sorry thats too hard for me

Step-by-step explanation:

As a backpack designer at a sportswear company, my team has been assigned the task of creating a smaller toddler size backpack and a larger teen size backpack based on our already popular kids model. In addition to designing these new backpacks, we will also create accessories that can be sold alongside them.

For the smaller toddler size backpack, our focus will be on ensuring a comfortable fit for young children while incorporating fun and age-appropriate designs. We will consider using lightweight and durable materials to make it easier for toddlers to carry. The backpack will have adjustable straps to accommodate their smaller frames and promote proper weight distribution. As for accessories, we can design detachable safety harnesses, featuring playful characters or animal shapes, to help parents keep their toddlers close in crowded places.

For the larger teen size backpack, we will prioritize functionality and style to cater to the needs and preferences of teenagers. The backpack will have ample storage compartments to accommodate textbooks, laptops, and other school essentials. We will also consider incorporating features like padded laptop sleeves, water bottle pockets, and headphone ports to enhance convenience and usability. To complement the backpack, we can design coordinating accessories such as pencil cases, lunch bags, and keychain attachments that match the overall design aesthetic.

Throughout the design process, we will ensure that both the toddler and teen size backpacks maintain the high quality and attention to detail that our brand is known for. Our team will carefully select fabrics, hardware, and zippers that are durable and long-lasting, considering the wear and tear expected in different age groups. We will also focus on ergonomic design principles to prioritize comfort and proper weight distribution for both the smaller and larger backpacks.

By expanding our backpack line to include smaller toddler and larger teen sizes, along with the accompanying accessories, we aim to provide functional, stylish, and age-appropriate options for a broader range of customers.

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Answer:

Number of push up = 8 + 2x

Step-by-step explanation:

Keenan can do 8 push ups each day. He plans to do 2 extra day until he is doing 30 push ups. Each day he does an additional 2 push up, on the first day he does 8 + 2 = 10 push up, on the second day he does 10 + 2 = 12 push ups. This can be represented by the expression:

Number of push up = 8 + 2x

where x is the number of days.

To do 30 push ups, we can calculate the number of days needed:

30 = 8 + 2x

2x = 30 - 8

2x = 22

x = 11

Answer:

8+2x its from khan academy

Step-by-step explanation:

give person above brainliest :)

The probability that x forms are required is known to be proportional to  c = 1/15.   c= 2/5  c= 3/5, c= 1.1

(a) Since the probabilities must sum to 1, we have:

pX(1) + pX(2) + pX(3) + pX(4) + pX(5) = c(1 + 2 + 3 + 4 + 5) = 15c

Therefore, c = 1/(1 + 2 + 3 + 4 + 5) = 1/15.

(b) The probability that at most three forms are required is:

P(X ≤ 3) = pX(1) + pX(2) + pX(3) = c(1 + 2 + 3) = 6c = 2/5.

(c) The probability that between two and four forms (inclusive) are required is:

P(2 ≤ X ≤ 4) = pX(2) + pX(3) + pX(4) = c(2 + 3 + 4) = 9c = 3/5.

(d) No, because the probabilities do not sum to 1:

Σ pX(x) from x = 1 to 5

= (1/50)(1 + 4 + 9 + 16 + 25)

= 55/50

= 1.1

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The null hypothesis states that the mean daily consumption of regular-coffee drinkers is equal to or greater than the mean daily consumption of decaffeinated-coffee drinkers. The alternative hypothesis states that the mean daily consumption of regular-coffee drinkers is less than the mean daily consumption of decaffeinated-coffee drinkers.

The null hypothesis (H0) and alternative hypothesis (H1) can be stated as follows:

H0: μ1 ≥ μ2 (The mean daily consumption of regular-coffee drinkers is equal to or greater than the mean daily consumption of decaffeinated-coffee drinkers)

H1: μ1 < μ2 (The mean daily consumption of regular-coffee drinkers is less than the mean daily consumption of decaffeinated-coffee drinkers)

Here, μ1 represents the population mean daily consumption of regular-coffee drinkers, and μ2 represents the population mean daily consumption of decaffeinated-coffee drinkers.

To test these hypotheses, we can conduct a two-sample t-test. We have the sample means, sample sizes, and population standard deviations for both groups. Using these values, we can calculate the test statistic and compare it to the critical value at the 0.010 significance level.

Let's calculate the test statistic:

t = (x1 - x2) / sqrt((s1^2/n1) + (s2^2/n2))

Where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Given the sample means and sample sizes, we can calculate the test statistic. If the test statistic falls in the critical region (i.e., below the critical value), we reject the null hypothesis and conclude that the mean daily consumption of regular-coffee drinkers is less than the mean daily consumption of decaffeinated-coffee drinkers.

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Answer:

-5 and -9 are the constants, can also be written -14

Answer:

The first one, since that is the only one showing in the screen,

and that is actually correct, since there are no intersecting points.

In RAND function, when we click anyplace in the succeed sheet use duplicate and afterward glue as values. returns an irregular number that is more noteworthy than or equivalent to 0 and under 1.

The subject of arithmetic incorporates amounts and their varieties, conditions and related designs, shapes and their areas, and where they can be found. The expression "function" alludes to the connection between a bunch of information sources, every one of which has a related result. An association among data sources and results in which each info prompts a solitary, particular outcome is known as a capability. Each capability is given a space and a codomain, or scope. Normally, f is utilized to signify capabilities (x). input is a x. There are four fundamental sorts of capabilities open. in view of the accompanying variables: on capabilities, coordinated capabilities, many-to-one capabilities, inside capabilities, and on capabilities.

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\(~~(x+5)(2x+3)-3(x-2)(6x+5)\\\\=2x^2 +3x + 10x +15 - (3x-6)(6x+5)\\\\=2x^2 +13x +15 - (18x^2 +15x -36x -30)\\\\=2x^2+13x+15-(18x^2 -21x-30)\\\\=2x^2 +13x+15-18x^2 +21x +30\\\\=-16x^2 + 34x+45\)

True. Exception reports show a greater level of detail than is included in routine reports.

Exception reports are reports that help in identifying data that does not conform to expected patterns. Exception reports show information about an exception in the data set.

This helps to identify irregularities or anomalies in data or system operations.Exception reports are used to analyze system performance, monitor resource consumption, and to detect unusual activity.

This type of report is important to identify issues or errors, where the routine reports or standard reports would not provide enough detail or insight to do so.

It provides detailed information on any unusual event or anomaly that occurred beyond the usual course of events or processes.Exception reports are generated and distributed when the data is not expected or when an event occurs that is outside of what is considered typical.

For example, a financial system might generate an exception report if a transaction is entered that exceeds the maximum allowed amount. This report would show the details of the transaction and highlight the exception.

The purpose of exception reports is to provide users with a higher level of detail than they would find in routine reports. Exception reports are used to highlight significant data, which will be used for further analysis or action.

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Answer:

x=17 degrees

Step-by-step explanation:

All 3 angles = 180 degrees

So 90 + 54 + (x+19) = 180

Combine like terms

163 + x = 180

Subtract 163 from both sides

x = 180-163

x = 17

Answer:

49.5

Step-by-step explanation:

you multiply the height and base then divide that awnser by 2

Answer:

the aanswer is 1

Step-by-step explanation:

There are approximately 494.25 cubic inches of sugar in the container.

We can use the formula for the volume of a cylinder to find the total volume of the container, and then multiply it by 1 3/4 to find the volume of sugar:

Volume of cylinder = π\(r^2^h\)

where r is the radius and h is the height.

From the measurements given, we have:

r = 3 inches

h = 5 inches

Substituting these values into the formula, we get:

Volume of cylinder = π\((3)^2(5) = 45\)π cubic inches

To find the volume of sugar, we can multiply this by 1 3/4, or 7/4:

Volume of sugar = (7/4)(45π) = 157.5π cubic inches

Using a calculator to approximate π to 3.14, we get:

Volume of sugar ≈ 494.25 cubic inches

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Answer:

15.7 ft cause 5  x 3.14 = 15.7

Step-by-step explanation:

The probability of a person calling when you're thinking of them is subjective and depends on factors such as the likelihood of thinking of the person and the likelihood of the person calling, making it challenging to provide a precise estimate.

a. Likelihood of thinking of the person at a randomly selected time of day: This depends on the nature of your relationship, recent interactions or memories with the person, emotional significance, and personal thoughts. You can assign a subjective probability based on your own observations and experiences.

b. Likelihood of the person calling at a randomly selected time of day: This depends on the person's behavior, communication patterns, availability, and other relevant factors. Again, this can be subjectively estimated based on your knowledge of the person and their tendencies.

c. Compelling evidence of the combined events: To determine if the combined events provide compelling evidence that it wasn't merely a chance occurrence, you would need to establish a baseline probability of the individual events occurring independently by chance. If the combined probability significantly deviates from the expected chance occurrence, it may suggest a non-random connection between your thoughts and the person's behavior. However, a single occurrence may not provide sufficient evidence, and multiple instances would be needed to establish a pattern.

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The pattern in y = x² exhibits a nonlinear increase in y as x increases, forming a U-shaped curve, while the pattern in y = 15 + x shows a linear increase in y as x increases at a constant rate.

The patterns in the equations y = x² and y = 15 + x differ in terms of the direction of change. In the equation y = x², the pattern shows an increase in y as x increases.

As x increases from negative to positive values, the corresponding y values also increase, forming a symmetric U-shaped curve. The rate of increase for y becomes steeper as x moves further away from zero.

On the other hand, in the equation y = 15 + x, the pattern shows a linear increase in y as x increases. As x increases, the corresponding y values increase in a straight line.

The rate of increase for y remains constant at one unit per increase in x. This linear pattern reflects a constant upward shift of the graph as x increases.

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Displacement is the length of the straight line drawn from an object’s initial position to the object’s final position

The term "displacement" refers to a change in an object's position. It is a vector quantity with a magnitude and direction. The symbol for it is an arrow pointing from the initial position to the ending position. For instance, if an object shifts from position A to position B, its position changes.

If an object moves with respect to a reference frame, such as when a passenger moves to the back of an airplane or a professor moves to the right with respect to a whiteboard, the object's position changes. This change in location is described as displacement.

The displacement is the shortest distance between an object's initial and final positions. Displacement is a vector. It is visualized as an arrow that points from the initial position to the final position, indicating that it has both a direction and a magnitude.

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Explanation: The y value does not change, so we have a rate of change of 0.

A slightly more lengthy explanation involves picking two points from this table. Each point is a different row.

Let's say we go with (5,-1) and (6,-1) as the two points.

Use them in the slope formula.

\((x_1,y_1) = (5,-1) \text{ and } (x_2,y_2) = (6,-1)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{-1 - (-1)}{6 - 5}\\\\m = \frac{-1 + 1}{6 - 5}\\\\m = \frac{0}{1}\\\\m = 0\\\\\)

The slope is 0, so the rate of change is 0.

The line through the given points in the table is a flat horizontal line. All horizontal lines have slope 0.

Side note: in the slope formula, we can have 0 in the numerator. But we can never have 0 in the denominator (since division by zero is undefined).

Answer:

0

Step-by-step explanation:

Answer:

78kg

Step-by-step explanation:

76×5= 380kg

380-72-74-75-81= 78kg

Answer:

290

Step-by-step explanation:

Area of Parrallelagram is B*H

24 * 15 = 360

Area of Triagnle is 1/2 B*H

1/2* 14* 10 = 70

Subtract area of triangle form area of parrallelagram

360- 70= 290

Answer:

80

Step-by-step explanation:

The formula for finding the volume of a rectangular prism is base x width x height- 10x4x2

Answer:

The answer is 140

The yellow part which is shaded is 14x10 which equals 140

The correct answer to the given question is d. 2n+1. The other options, such as 1n, 3n, 2n-1, and 2n+2, do not accurately represent the chromosome number of a trisomic organism.

A trisomic organism is one that has an extra copy of a chromosome in its genome. This means that it has three copies of a particular chromosome instead of the usual two, which can have significant implications for the organism's development and health.

In terms of algebraic notation, the chromosome number of a trisomic organism would be denoted as 2n+1, where "n" represents the normal diploid number of chromosomes for that organism. The "2n" represents the normal two sets of chromosomes, and the "+1" represents the extra chromosome.

Therefore, the correct answer to the given question is d. 2n+1. The other options, such as 1n, 3n, 2n-1, and 2n+2, do not accurately represent the chromosome number of a trisomic organism. It is important to note that trisomies can occur for any chromosome, not just the sex chromosomes, and can have varying effects depending on which chromosome is affected.

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1. Since triangle ABC and DEF are congruent, the value of x is -3

2. length AB = 24

length DE = 24

If the three angles and the three sides of a triangle are equal to the corresponding angles and the corresponding sides of another triangle, then both the triangles are said to be congruent.

Since triangle ABC is congruent to triangle DEF , then we can say that line AB is equal to line DE

therefore;

12- 4x = 15-3x

collect like terms

12 -15 = -3x +4x

x = -3

therefore the value of x is -3 and

AB = 12 - 4x

AB = 12 -4( -3)

AB = 12 +12 = 24

DE = 15-3x

= 15-3(-3)

= 15 + 9

= 24

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Answer:

13/24

Step-by-step explanation:

First we create a common denominator by multiplying the denominators of 8 and 3 to get 24. Now we convert the two given fractions

\( \frac{1}{8} = \frac{3}{24} \)

\( \frac{1}{3} = \frac{8}{24} \)

A full circle is 24/24. Now all we do is subtract

\( \frac{24}{24} - \frac{8}{24} - \frac{3}{24} = \frac{13}{24} \)

Answer:

13/24

Step-by-step explanation:

1-11/24

=

13/24

Answer:

10w + 35 >= 125

Step-by-step explanation:

She saves $10m per week. That is 10w.

She already has $35, so add 35 to 10w.

10w + 35 >= 125