A student solves the following equation and determines that the solution is −2. Is the student correct? Explain. 3 a 2 − 6a a2 − 4 =.

Hence,  when \(n=10\) the given inequality is true.

What is the inequality?

An inequality is said to be sharp if it cannot be relaxed and still be valid in general.

Here given that,

Which integer will make the inequality \(2(n + 2) < 5(n -1)\) true.

So,

\(2(n + 2) < 5(n-1)\)

When

\(n=10\\\\\\2(10+2) < 5(10-1)\\\\2(12) < 5(9)\\\\24 < 45\)

Hence,  when \(n=10\) the given inequality is true.

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(a) Construct confidence intervals are : 90%: [428.95, 444.05], 95%: [427.13, 445.87], 99%: [423.67, 449.33].

(b) The 99% confidence interval has the widest interval.

(a) To construct confidence intervals for the mean breaking strength of the wool fibers, we shall use the given formula:

Confidence interval = sample mean ± (critical value * standard error)

The critical value here will depends on the level of confidence. For a 90% confidence level, the critical value is 1.645 (from the standard normal distribution). For a 95% confidence level, the critical value is 1.96, and for a 99% confidence level, the critical value is 2.576.

Standard error is obtained by dividing the sample standard deviation by the square root of the sample size.

Plugging in the values, we can calculate the confidence intervals:

90% confidence interval:

Lower bound = 436.5 - (1.645 * (11.9 / √20))

Upper bound = 436.5 + (1.645 * (11.9 / √20))

95% confidence interval:

Lower bound = 436.5 - (1.96 * (11.9 / √20))

Upper bound = 436.5 + (1.96 * (11.9 / √20))

99% confidence interval:

Lower bound = 436.5 - (2.576 * (11.9 / √20))

Upper bound = 436.5 + (2.576 * (11.9 / √20))

(b) The width of a confidence interval depends on both the critical value and the standard error. When aiming for a higher level of confidence, the interval becomes wider as it requires a larger critical value. Consequently, it can be concluded that among the given confidence intervals, the one with a 99% confidence level will have the broadest range.

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According to the information we can infer that Dora's conclusion may be incorrect because the information provided only states that the number of people who spent time reading falls within specific ranges (0-2 hours, 2-4 hours, and 2-10 hours), but it does not give a specific count for those who spent at least 4 hours. Therefore, Dora's assumption that "most people spent at least 4 hours a week reading" is not supported by the given data.

The range of the time spent reading cannot be determined from the information provided because the ranges are overlapping. For example, a person who spent exactly 2 hours reading could fall into both the first range (0-2 hours) and the second range (2-4 hours). Without more specific data or non-overlapping ranges, it is not possible to determine the exact range of time spent reading.

To estimate the mean time spent reading by Dora's friends, we can calculate the midpoint of each range and use it as an approximate value. The midpoint for the first range (0-2 hours) is 1 hour, for the second range (2-4 hours) is 3 hours, and for the third range (2-10 hours) is 6 hours. We can then calculate the estimated mean by taking the weighted average of these midpoints using the respective number of people as weights.

Estimated mean = [(4 * 1) + (5 * 3) + (11 * 6)] / (4 + 5 + 11) = 4.53 hours (approximately)

So, an estimate of the mean time spent reading by Dora's friends is approximately 4.53 hours.

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Answer:

Measure 1 is 112º

You know that 112º is the closest answer because you can see the angle is obtuse. And obtuse is an angle less than 180 but more than 90º

Step-by-step explanation:

So a straight line is equal to 180º so just set the equations equal to 180. Your final equation should look like (3x + 22) + (2x + 8) = 180

Now all you have to do is solve for x.

3x + 22 + 2x + 8 = 180

Combine like factors

3x + 2x = 5x

22 + 8 = 30

Now your equation should look like 5x + 30 = 180

Subtract 30 from both sides.                   -30       -30  

                                                                            ----------

                                                                                150

So now the equation should look like 5x = 150

Divide both sides by 5, 150/5 = 30

SO x = 30

Plug 30 in to the equation to check your answer

(3*30 + 22) = 112

(2*30 + 8) = 68

112 + 68 = 180

Answer:

and also mark me the brainliest for the answer

Step-by-step explanation:

Answer:

20.8

Step-by-step explanation:

tan = opposite/ adjacent

opposite = tan * adjacent

opposite = 1,482561 * 14 = 20,755854

Answer:

20.8 =x

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp / adj

tan 56 = x/ 14

14 tan 56 =x

20.75585356 =x

To the nearest tenth

20.8 =x

Answer:

The answer to this problem is True.

The first series, ∑[n=1 to ∞] 7/(8n+3)n, converges. The second series, ∑[n=1 to ∞] (−1)nn^2(n+2)!/n!32n, also converges.

For the first series, ∑[n=1 to ∞] 7/(8n+3)n, we can use the ratio test to determine convergence. Taking the limit of the ratio of consecutive terms, we get lim(n→∞) [(7/(8(n+1)+3))/(7/(8n+3))] = 8/9. Since the limit is less than 1, by the ratio test, the series converges.

For the second series, ∑[n=1 to ∞] (−1)nn^2(n+2)!/n!32n, we can use the ratio test as well. Taking the limit of the ratio of consecutive terms, we get lim(n→∞) [((-1)^(n+1)(n+1)^2((n+3)!)^2)/((n+1)!^2 * (3(n+1))^2)] = 0. Since the limit is less than 1, by the ratio test, the series converges.

Therefore, both series converge based on the ratio test.

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Answer:

2x1/6

Step-by-step explanation:

Answer:

\((5)(\frac{1}{2})\\\)

Step-by-step explanation:

If we will look at the picture we will notice that each triangle has half of it shaded in with red and there are 5 triangles. From this I conclude that the answer is \((5)(\frac{1}{2})\)

The lowest point on the graph occurs at point (3π/2,  -1)

One of the three fundamental functions in trigonometry, along with cosine and tan functions, is the sine function.

The ratio of the opposite side of a right triangle to its hypotenuse is known as the sine x or sine theta.

The sine function graph is sinusoidal in nature. This is a sim=ne wave that have smooth periodic oscillation

The attached graph shows sine function graph plotted with the interval [0, 2pi]

The lowest point is observed to occur at  (3π/2,  -1)

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Answer:

-0.375

Step-by-step explanation:

You can write fractions as equations and solve for a decimal.

-3/8 = -3 ÷ 8

-3 ÷ 8 = -0.375

Answer:

I got you bro

Step-by-step explanation:

-0.38

Answer:

15 days

Step-by-step explanation:

Don't you mean 1/3?  If so,

 5 cans

-------------------- = 15 days

1/3 can/daily

So, the probability that a randomly selected cell phone that has been recalled came from site 3 is 2.5 or 25%.

We can use Bayes' theorem to calculate the probability that a phone that has been recalled came from site 3. Bayes' theorem states that:

P(A|B) = P(B|A) * P(A) / P(B)

where:

P(A|B) is the probability of event A occurring given that event B has occurred (in this case, the probability that a phone came from site 3 given that it has been recalled)

P(B|A) is the probability of event B occurring given that event A has occurred (in this case, the probability that a phone has been recalled given that it came from site 3)

P(A) is the prior probability of event A occurring (in this case, the probability that a phone came from site 3)

P(B) is the prior probability of event B occurring (in this case, the probability that a phone has been recalled)

So, in this case, we have:

P(site 3 | recalled) = P(recalled | site 3) * P(site 3) / P(recalled)

We know that:

P(recalled | site 3) = 9%,

P(site 3) = 10%

We also know that:

P(recalled) = P(recalled | site 1) * P(site 1) + P(recalled | site 2) * P(site 2) + P(recalled | site 3) * P(site 3)

= (5% * 60%) + (7% * 30%) + (9% * 10%) = 3% + 2.1% + 0.9% = 6%

So, we can now calculate the probability that a phone that has been recalled came from site 3 as:

P(site 3 | recalled) = (9% * 10%) / 6% = 0.15 / 0.06 = 2.5

So the probability that a randomly selected cell phone that has been recalled came from site 3 is 2.5 or 25%.

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Taylor polynomials of degree 2 and 3 centered at x = 0 for the function f(x) = 16tan(x) are:

P2(x) = 16x + 8x^2

P3(x) = 16x + 8x^2

To find the Taylor polynomials centered at x = 0 for the function f(x) = 16tan(x), we can use the Taylor series expansion for the tangent function and truncate it to the desired degree.

The Taylor series expansion for tangent function is:

tan(x) = x + (1/3)x^3 + (2/15)x^5 + (17/315)x^7 + ...

Using this expansion, we can find the Taylor polynomials of degree 2 and 3 centered at x = 0:

Degree 2 Taylor polynomial:

P2(x) = f(0) + f'(0)(x - 0) + (1/2!)f''(0)(x - 0)^2

= 16tan(0) + 16sec^2(0)(x - 0) + (1/2!)16sec^2(0)(x - 0)^2

= 0 + 16x + 8x^2

Degree 3 Taylor polynomial:

P3(x) = P2(x) + (1/3!)f'''(0)(x - 0)^3

= 0 + 16x + 8x^2 + (1/3!)(48sec^2(0)tan(0))(x - 0)^3

= 16x + 8x^2

Therefore, the Taylor polynomials of degree 2 and 3 centered at x = 0 for the function f(x) = 16tan(x) are:

P2(x) = 16x + 8x^2

P3(x) = 16x + 8x^2

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Answer:

Step-by-step explanation:

60 hours in a minute.

150/60=2.5 hours

hope this helps

We can calculate that 150 munites is equivalent to 2.5 hours using the conversion factors.

A conversion factor, or a formula that shows how the units relate to one another, can be used to change the units of a measured quantity without changing the value.

A conversion ratio (or unit factor) will always have a numerator and a denominator that are the same number expressed in different units (1).

One unit of measurement can be converted into another using conversion factors.

Changes from the company's single-entry accounting system to a double-entry one are part of the conversion process.

So, we already have the knowledge that:

60 min = 1 hour

Then,

150 min = 2.5 hours

Therefore, we can calculate that 150 munites is equivalent to 2.5 hours using the conversion factors.

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Let x and y the numbers we are looking for, since they have a sum of 23, we can set the following equation:

Also, since its difference is 9, we can set the following equation:

Adding the first equation to the second one we get:

Simplifying the above equation we get:

Dividing the above equation by 2 we get:

Substituting x=16 in the first equation we get:

Subtracting 16 from the above equation we get:

Answer: The numbers we are looking for are 16 and 7.

Answer:

The two numbers are 7 and 16.

Step-by-step explanation:

Answer:

Monkey says NO

Step-by-step explanation:

Monkey says A^2 + B^2 = C^2. Monkey do math, gets C = 8.5. So close, monkey sad. Not right triangle.

This is impossible to solve.

For an equation or inequality to be solvable, there must be the same number of inequalities as variables. Here, there is an x and there is a y. This means that you need at least two inequalities to solve it.

You can, however, rearrange to get x or y on one side.

This can be done for x:

5x < 10 + 2y

x < 2 + 2/5y

Or it can be done for y:

5x < 10 + 2y

5x - 10 < 2y

2.5x - 5 < y

Answer:

B

Step-by-step explanation:

I did some maths

Answer:

hi i think the answer shouldbe 34/43 as its out of 43 and there is 34 people on the internet. I think this should be write but it may  be wrong. if this is right please vote for brainliest. i hope my answer is right and this helps bye.

Answer:

3

Step-by-step explanation:

The slope of the given line is \(\frac{2}{3}\).

If a line passes through two points (x₁, y₁) and (x₂, y₂) respectively, then slope of the line is \(m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

Here, the given line passes through points (0, 6) and (-9, 0).

Therefore, the slope of this line is (m)

\(= \frac{0 - 6}{-9 - 0}\\= \frac{6}{9} \\= \frac{2}{3}\)

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Answer:

The probability of rolling an odd number or a two on a six-sided die is 1/2 + 1/6 = 2/3. This means that if you roll a six-sided die 300 times, you can expect to roll an odd number or a two approximately 200 times

Step-by-step explanation:

Answer: 400 TIMES

Step-by-step explanation:

1/6 +1/2

4/6

2/3

The only number that is 10 times as much as 72 is 720.

To find the numbers that are 10 times as much as 72 or 1/10 of 72, we can perform the following calculations:

10 times 72 = 720

1/10 of 72 = 7.2

So, the numbers that are 10 times as much as 72 are 720.

The number 67 is not 10 times as much as 72 or 1/10 of 72. Therefore, it is not one of the numbers we are looking for.

On the other hand, 1/10 of 72 is 7.2, which is not one of the numbers we are looking for either.

Therefore, the only number that is 10 times as much as 72 is 720.

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complete question

Select all the numbers that are 10 times as much as 72, 67, or 1/10 of 72.

- 67

-46

-720

-480

In 1981 number of ways a committee of five members of the department if at least one woman must be on the committee.

By choosing some items from a set and creating subsets, permutation and combination are two approaches to express a collection of things. It outlines the numerous configurations for a certain set of data. Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented. Both ideas are critical to mathematics.

The number of ways of picking 5 from 14 is what the question is actualy asking minus combinations of 5 from 7 , because there must be 1 woman

so 5 from 14 is given by :

= \(\frac{14*13*12*11*10}{5*4*3*2*1}\)

which is :

14 x 13 x 11 = 2002

combinations of 5 from 7 is :

(9x8x7x6x5) / (5x4x3x2x1)

\(\frac{7*6*5*4*3}{5*4*3*2*1}\)

which is :

7 x 3= 21

so the final answer is 2002 - 21 = 1981.

Therefore, in 1981 ways a committee of five members of the department if at least one woman must be on the committee.

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Answer:

5,9

Step-by-step explanation:

To determine which gym membership is more cost-effective, you would need to compare the total cost for a given period. Let's consider a time frame of one month.

For Gym A, the monthly payment is $50. This means that regardless of how many times you visit the gym, you will pay a fixed amount of $50 each month.

For Gym B, the cost is $10 per visit. To calculate the total cost for a month, you need to estimate the number of times you plan to visit the gym in that period. Let's assume you plan to visit the gym 10 times in a month.

The total cost for Gym B would then be calculated as:

Total Cost for Gym B = Number of Visits * Cost per Visit

Total Cost for Gym B = 10 visits * $10 per visit

Total Cost for Gym B = $100

Comparing the total costs, we find that for Gym A, the monthly payment is $50, and for Gym B, the estimated cost for 10 visits is $100. In this case, Gym A would be the more cost-effective option if you plan to visit the gym at least 10 times in a month. However, if you anticipate visiting the gym less than 10 times in a month, Gym B might be the more affordable choice.

By using basic arithmetic to calculate the total costs based on the given pricing structures, you can make an informed decision regarding the gym membership that fits your budget and lifestyle.

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The probability of getting an no head is 1/8 or 12.5%

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

Probability = sample space / total outcome

The total outcome of tossing a coin thrice is 8

The sample space of getting no head i.e (TTT) is 1

Therefore the probability of getting no head = 1/8

in percentage; 1/8 × 100 = 100/8 = 12.5 %

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Answer:

Step-by-step explanation:

i know

Certify Completion Icon Tries remaining: 3 A high school has 52 players on the football team. The summary of the players' weights is given in the box plot. The median weight of the players on the football team is 160 pounds.

The box plot shows that the median weight of the players is the middle value of the distribution. In this case, the median weight is halfway between the 26th and 27th players, which is 160 pounds.

The box plot also shows that the minimum weight of the players is 150 pounds and the maximum weight is 212 pounds. The interquartile range, which is the range of the middle 50% of the data, is 20 pounds.

In conclusion, the median weight of the players on the football team is 160 pounds. This means that half of the players on the team weigh more than 160 pounds and half of the players weigh less than 160 pounds.

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