the sum of two number is 1 is and their difference 56.
what are the numbers?

The width of the confidence interval reduces as the decrease the number in sample. The width increases as the standard deviation increases. The width increases as the confidence level increases. The width increases as the significance level decreases.

A confidence interval is defined as the range of values that we observe in our sample and for which we expect to find the value that accurately reflects the population.

The width of a confidence interval,

W = 2 * CV * \(\frac{SD}{\sqrt{n} }\)

It depends on three things,

To decrease the width the following options can be used:

Increasing the value of n will result in a decrease in the width of the confidence interval because the sample is inversely proportional to the width.

The width of the confidence interval is exactly proportional to the standard deviation. The interval's breadth will likewise shrink as the standard deviation value is reduced.

The confidence level determines the distribution's critical value. The crucial value will be higher the higher the confidence level.

Hence, as the confidence level is decreased, the critical value will as well, resulting in a reduction in the width of the interval.

Therefore,

The width of the confidence interval reduces as the decrease number in sample.

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Answer:

hope these help........

Answer:

\(x = \frac{-3}{4}\) or  \(x = \frac{3}{2}\)

Step-by-step explanation:

\(8x^{2} - 4x = 2x +9\)

Okay, let's put everything on one side.

\(8x^{2} -4x-2x-9=0\)

As you can see we can subtract -4x from -2x now leaving us with -6x.

\(8x^{2} -6x-9=0\)

Now there are multiple ways to solve a polynomial, but we can go with a way to factor them the easy way. We need to multiply the leading coefficient with the ending term because there is no common number we can factor out of these guys.

\(8(-9)=-72\)

We multiplied 8 and -9 together which gave us -72. With this, we need to find two numbers that add to the middle term, -6, but will multiply to -72. This is going to be 6 and -12. Now we are going to replace the middle coefficient with those two numbers.

\(8x^{2} + 6x - 12x- 9= 0\)

(Keep in mind the equation has not changed)

Now we are going to do something called factoring by grouping, with the first two terms, 8x^2 and 6x we take out the GCF (greatest common factor):

\(2x(4x+3)\)

so let's do the same between the last two.

\(-3(4x+3)\)

So when putting them together we have,

\(2x(4x+3)-3(4x+3)=0\)

Now let's factor here, (4x+3) can be taken out and 2x as well as -3 can be put together.

\((4x+3) (2x-3)=0\)

Then we set these factors to zero to get our x answer:

\(4x+3=0\)

\(2x-3=0\)

And we solve, which leaves us with:

\(x = \frac{-3}{4}\) or  \(x = \frac{3}{2}\)

A recursive sequence is a sequence in which terms are defined using one or more previous terms that are given.

If you know the term n of an arithmetic sequence and you know the common difference, d, you can find the term \((n + 1)\) by tossing the recursive formula to \(n + 1 = a \ n + d\)

We have then:

\(5, 15, 30, 50\)

\(an = (\dfrac{5}{2} ) \times (n) \times (n + 1)\)

Answer:

the recursive formula for 5, 15, 30, 50, is:

an = (5/2) x (n) x (n + 1)

Answer:

B) $73

Step-by-step explanation:

add all of your values and divide by the amount of values

52+55+55+55+59+64+66+68+72+73+73+73+73+75+81+81+83+84+84+86+87=

1,499

1,499 divided by 21 = 71.3809523...

which rounds to 73

HOPE THIS HELPS!!! :)

The median is of $48 in the stem leaf plot and option B is correct.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

The median of a data-set is the value that separates the bottom 50% from the upper 50% of values.

The graph has 16 values, already ordered.

It is an even number, hence the median is the mean of the 8th and the 9th values, which considering the key are both 48,

Hence, the median is of $48 and option B is correct.

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Stem-and-Leaf Plot shows the amount of money each student spends

on travel per day in dollars. What is the median for the data in this graph?

Stem Leaf

A) $35

B) $48

C) $53

D) $54

Answer:

1,6

Step-by-step explanation:

1,6 thats how

The volume of the solid is approximately 1.04 x 10⁻¹⁰ cubic units.

To find the volume of the solid obtained by rotating the region bounded by the y=1/x⁵, y=0, x=1, x=9 about the y axis, we can use the Disk Method.

The Disk Method can be used when rotating a function around an axis. It requires integration to find the volume of the solid. The formula for the Disk Method is: V=π∫aᵇ(R(x))²dx where R(x) is the radius of the disk.

In this case, the y-axis is our axis of revolution and the function is given as y=1/x⁵ and the limits of integration are 1 and 9. Thus, the formula becomes V=π∫1⁹(1/x⁵)²dx. After simplifying, this becomes V=π∫1⁹ 1/x¹⁰ dx.

Evaluating this integral, we get V=π[1/(-9x⁹)] from 1 to 9. This simplifies to V=π[1/(-9(9)⁹) - 1/(-9(1)⁹)] or V=π[1/3,025,611,125].

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Answer:

1.95

Step-by-step explanation:

area = (1/2 ×1 ×1 )×3 = 1.5 ( for sides)

area = ( 1/2 ×1 ×0.9) = 0.45 for base

area =1.5+0.45 = 1.95

Answer:

They have the same measure (degrees)

Step-by-step explanation:

A central angle and its intercepted arc have the same measure.

A central angle has its vertex at the center. Think of a clock. You can make an angle with the hands of a clock. The angle and the piece of the circle that the angle cuts off (the intercepted arc) are the same! Like 20° and 20° or

180° and 180° or

67° and 67°

The probability of the carpet having no flaws is 0.431.

The area of the given carpet is 9 × 14 = 126 square feet, the probability that a carpet contains no flaws is given by:P(X = 0) = e−λ λ^X / X!Where λ = the rate of occurrence of flaws and X = the number of flaws in a given area of a carpet. Hence,λ = 1 flaw / 150 sq. ft. = 126 / 150 = 0.84X = 0

The probability of a carpet having no flaws isP(X = 0) = e−0.84 (0.84)^0 / 0! = 0.431The probability that a carpet that is 9 feet by 14 feet contains no flaws is 0.431.

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Answer:

-3

Step-by-step explanation:

-7+4=-3

The absolute value of -3 is 3

The negative sign in front of the absolute value bracket makes it -3

Answer:

x = -3

Step-by-step explanation:

Step 1: Simplify signs

3x + 7 = -2

Step 2: Subtract 7 on both sides

3x = -9

Step 3: Divide both sides by 3

x = -3

Answer:

11.43 seconds

Step-by-step explanation:

80/7 = 11.428 = 11.43( nearest hundredth)

The greatest possible length of the line segment joining two points on the circle is 8 cm, which is equal to the diameter of the circle.

The greatest possible length of a line segment joining two points on a circle is equal to the diameter of the circle.

In this case, the circle has a radius of 4 cm. The diameter of a circle is twice the length of the radius. Therefore, the diameter of this circle is 2 * 4 cm = 8 cm.

Hence, the greatest possible length of the line segment joining two points on the circle is 8 cm, which is equal to the diameter of the circle.

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Given a function of two variables, n and k, denoted as h(n, k), the function describes a mathematical relationship or operation that depends on the values of both n and k. Further details about the specific function, its definition, or purpose are required to provide a more comprehensive explanation.

A function of two variables, h(n, k), typically represents a mathematical relationship or operation that involves two independent variables, n and k. The specific form and purpose of the function can vary widely depending on the context or problem at hand.

To understand the behavior and properties of the function h(n, k), additional information is needed. This may include the mathematical expression defining the function, any constraints or conditions on the variables, and the intended interpretation or application of the function.

The function h(n, k) could represent various scenarios, such as a cost function in economics, a probability distribution in statistics, or a mathematical model in a scientific context. Without more details, it is challenging to provide a specific explanation or analysis of the function and its implications.

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10 maybe? I don't really know but maybe 10 will be right?????

Answer:

i think its 1/8

Answer:

1/8

Step-by-step explanation:

Answer:

  False

Step-by-step explanation:

You want to know if it is true that the graph of a rational function cannot cross a horizontal asymptote.

Once a function is on its final approach to an asymptote, it will approach, but not cross, that asymptote.

The function may have a variety of behaviors prior to that point, so may cross the horizontal asymptote one or more times before its final behavior is established.

An example with the asymptote y = 0 is attached.

<95141404393>

Answer:

Bearing in the mind that an ossicle triangle has twin sides and coming out of the vertex they make twin angles at the base check the picture out

Step-by-step explanation:

Same way with 42

Answer:

x = 46°

Step-by-step explanation:

Angles on a straight line sum to 180°.

Therefore, the interior angle of the triangle that forms a linear pair with the exterior angle marked 130° is:

⇒ 180° - 130° = 50°

The interior angle of the triangle that forms a linear pair with the exterior angle marked 96° is:

⇒ 180° - 96° = 84°

The interior angles of a triangle sum to 180°. Therefore:

⇒ 50° + 84° + x = 180°

⇒ 134° + x = 180°

⇒ 134° + x - 134° = 180° - 134°

⇒ x = 46°

Therefore, the size of angle x is 46°.

The number of individuals in Chicago that will respond positively to Program 2 is 22 out of 25.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.

Given that the chances of a positive response from Chicago residents to two government programs are 65.9% for Program 1 and 87.5%  for Program 2, the likelihood of a positive response for Program 2 given that the person is from Los Angeles must be calculated as follows:

87.5 100 = X

43.75 / 50 = X

21.875 / 25 = X

Therefore, 22 out of 25 individuals in Chicago  will respond positively to Program 2.

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A z-score, also known as a standard score, is a measure of how many standard deviations an individual data point is away from the mean of a distribution.

a) To determine whether the design criterion is satisfied using Chebyshev's inequality, we can apply the formula:

P(|X - μ| ≤ kσ) ≥ 1 - 1/k²Where:

P is the probability

X is the random variable (in this case, the exam grade)

μ is the mean (77%)

σ is the standard deviation (square root of the variance, which is √9% = 3%)

Let's calculate the probability of an exam grade being within 4.5% of the mean:

P(|X - 77| ≤ 0.045 * 77) ≥ 1 - 1/(0.045)²

P(|X - 77| ≤ 3.465) ≥ 1 - 1/0.002025

P(|X - 77| ≤ 3.465) ≥ 1 - 494.382

P(|X - 77| ≤ 3.465) ≥ -493.382

The inequality states that the probability of an exam grade being within 4.5% of the mean is greater than or equal to -493.382. Since probabilities are always between 0 and 1, this inequality does not hold. Therefore, the design criterion is not satisfied using Chebyshev's inequality.

b) If we assume that the retrieval time is normally distributed with a mean of 77% and a variance of 9%, we can use the properties of the normal distribution to determine if the design criterion is satisfied.

To find the probability of an exam grade being within 4.5% of the mean, we need to calculate the z-scores corresponding to the lower and upper limits of the range.

For the lower limit:

z_lower = (x_lower - μ) / σ

= (77 - 77) / √9

= 0

For the upper limit:

z_upper = (x_upper - μ) / σ

= (77 + 4.5 - 77) / √9

= 0.5 / 3

= 0.1667

Using a standard normal distribution table or calculator, we can find the area under the curve between

z = 0 and

z = 0.1667.

The probability of the exam grade falling within this range is the difference between the cumulative probabilities at these two z-values.

P(|X - 77| ≤ 4.5%) = P(0 ≤ Z ≤ 0.1667)

From the standard normal distribution table, the probability for this range is approximately 0.0659. Since this probability is less than the desired probability of 90%, the design criterion is not satisfied if the retrieval time is normally distributed with a mean of 77% and a variance of 9%

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The criterion requires at least 90% of the data to fall within 4.5% of the mean, which is within 1.5 standard deviations, we can see that the design criterion is satisfied.

a) Chebyshev's inequality is a mathematical formula that can be used to establish the proportion of data that falls within a certain number of standard deviations from the mean. According to Chebyshev's inequality, at least (1 - 1/\(k^2\)) of the data lies within k standard deviations of the mean, where k is any positive number greater than 1.
In this case, the criterion requires that at least 90% of all Probability Final Exams not differ from the mean by more than 4.5%. This means that we need to find the value of k such that at least 90% of the data falls within k standard deviations of the mean.
To do this, we can use Chebyshev's inequality. Since we know the variance is 9%, the standard deviation is the square root of the variance, which is √9 = 3.
Let's calculate the value of k:
k = (4.5/3) = 1.5
Now, we can use Chebyshev's inequality to determine the proportion of data that falls within 1.5 standard deviations of the mean:
(1 - 1/\(k^2\)) = (1 - 1/\(1.5^2\)) = (1 - 1/2.25) = (1 - 0.4444) = 0.5556
So, according to Chebyshev's inequality, at least 55.56% of the data falls within 1.5 standard deviations of the mean. Since this is less than the required 90%, the design criterion is not satisfied.

b) If it were known that the retrieval time is normally distributed with a mean of 77% and a variance of 9%, we can use the properties of the normal distribution to determine if the design criterion is satisfied.
In a normal distribution, approximately 68% of the data falls within 1 standard deviation of the mean, 95% falls within 2 standard deviations, and 99.7% falls within 3 standard deviations.

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Answer:

a. 12 sides

b. Not possible

Step-by-step explanation:

a.

\(d=\frac{1}{2} n(n-3)\)

\(\frac{1}{2}n^{2}-\frac{3}{2} n=54\)

multiply by 2

\(n^{2} -3n=108\)

equation

\(n^{2} -3n-108=0\)

factor

\((n-12)(n+9)\)

\(n-12=0\\n=12\)

b.

\(n^{2} -3n=33\)

\(n^{2} -3n-33=0\)

The roots of the equation are decimal numbers

The number of sides must be integer

So there is no polygon with 33 diagonals.

Hope this helps

ANSWER:

+ 4 7/8

STEP-BY-STEP EXPLANATION:

Assuming that we start in week 0, with a total of 0 points, we must operate the changes in each week and the value opposite to that result must be the change necessary to return to the original value.

Just like that:

Which means that to return to the initial value, 4 7/8 points must be added

True. Using polynomial models in RD can produce bumps at the cutoff that are larger than they should be, which is known as the "overshoot" problem.

This happens because polynomial models are flexible and can fit high-frequency variations in the data, including noise, which can lead to an overfit of the data near the cutoff and create larger bumps than what should be expected.

To avoid this problem, alternative modeling strategies, such as local linear regression or spline-based models, can be used

True. Using polynomial models in RD can produce bumps at the cutoff that are larger than they should be, which is known as the "overshoot" problem.

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Answer:

I think it is

1: 22.37

2:16.81

3:83.16

Step-by-step explanation:

Answer:

Shape 1: 22.365

Shape 2: 16.81

Shape 3: 83.16

Step-by-step explanation:

I'm going to start with 2, because its the easiest shape to do, which is 4.1*4.1= 16.81. Next is 3, which you find the length by adding 4.1 to 9.1 = 13.2. You then multiply 13.2 by 6.3 = 83.16. Finally for shape 1, you first find the bottom shape,  which you do by dividing 6.3 by 2 so you can get the width of half the triangle. That is 3.15. then you multiply that by 7.1 to get the area of 22.365.

The Pythagorean Theorem is explained in this problem.

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is expressed as follows:

c² = a² + b².

In which:

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Charlie

Here, we want to check if polynomials is closed under subtraction or not

To check this, we proceed either ways, if the answer is same, then it is closed. If otherwise, then it is not

We have;

As we can see, both results are not equal

If subtraction was closed under polynomials, then the results of both should have been equal. This means Charlie is correct.

Answer:

all except the last one

Step-by-step explanation:

Answer:

n= -2

Step-by-step explanation:

3(4n+5)=-7n-23

expand brackets

12n + 15 =-7n-23

collect like terms

12n + 7n= -23-15

19n= -38

dividing throughout by 19

19n/19=-38/19

n= -2

Answer:

n = -2

Step-by-step explanation:

3(4n+5)= -7n -23

Distribute the 3,

12n + 15 = -7n -23

subtract 15 from both sides,

12n = -7n -38

add 7n to both sides,

12n + 7n = -38

simplify,

19n = -38

divide both sides by 19,

n = -2