If scores on the wechsler adult intelligence scale (wais) are normally distributed, with a mean of 100 and a standard deviation of 15, what percentage of scores will fall between 85 and 115

Answer:

\(x(x {}^{2} - 8x - 20) = 0\)

Use the quadratic formula to simply the second degree equation;

\(x(x + 2)(x - 10)\)

\(x1 = 0\)

\(x2 = - 2\)

\(x3 = 10\)

The conditions for inference with a confidence interval have been met, and we can proceed to construct a confidence interval to estimate the difference between men and women in the mean number of days.

What is confidence interval ?

A confidence interval is a range of values that is likely to contain the true value of a population parameter with a certain level of confidence.

To determine if the conditions for inference with a confidence interval have been met, we need to check the following assumptions:

Since the sample sizes are greater than 30 for both men and women, we can assume normality based on the Central Limit Theorem.

Also, since the samples are selected independently and randomly, the assumption of independence is met.

Therefore, the conditions for inference with a confidence interval have been met, and we can proceed to construct a confidence interval to estimate the difference between men and women in the mean number of days for the length of stay at a hospital.

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Answer:

B

Step-by-step explanation:

Area = length x width

Total surface area

=2(8*3) + 2(10*3) + 2(10*8)

=48+60+160

=268

"Given :  a survey was conducted in a group of 100 students of a school. the ratio of students who like mathematics and computer is 3:5. if 30 of them like both subjects and 10 of them like none of them,

To Find : number of students who like:  at most one subject.

Solution:

Mathematics = 3k

Computer = 5k

30 of them like both subjects

10 of them like none of them

Total = Math + Computer - Both  + None

100 = 3k  + 5k   - 30  + 10

=> 120 = 8k

=> k = 15

Mathematics = 45

Computer =  75

Mathematics only   = Mathematics - Both = 45 - 30 = 15

Computer only  = Computer - Both =75 - 30  = 45

at most one subject  = 100 - Both subjects 100 - 30  =  70

or none + computer only + Mathematics only = 10 + 45 + 15 = 70

70 Students like at most one subject"

To find if a relation is a function, identify if there is more that one value of y for the same value of x (if there are more than one value for one value of x is not a function)

Ordered pairs (x,y)

1.

x y

1 -2

-2 0

-1 2

1 3

2.

x y

1 1

2 2

3 5

4 10

5 15

Answer:

A : (146-4b)=(122-1b)

Step-by-step explanation:

Answer:

11. y=2x-1

11a. you subtract 2 from the y and 1 from the x and draw your points accordingly to go down or you add 2 to the y and add 1 to the x to go up and plot the points accordingly or you could just draw a graph like i did if you dont wanna do it by math lol. :)

11b. oh i guess i already answered this but y=2x-1

Step-by-step explanation:

pls mark brainliest tho ❤

Answer:

x= -3/2y + 6

Step-by-step explanation:

Let's solve for x.

2x+3y=12

Step 1: Add -3y to both sides.

2x+3y+−3y=12+−3y

2x=−3y+12

Step 2: Divide both sides by 2.

2x

2

=

−3y+12

2

First, let's calculate the z-score for the value 2.025 liters using the formula:

z = (x - μ) / σ

Where:

x = the value we want to calculate the probability for (2.025 liters)

μ = the mean of the process (2.050 liters)

σ = the standard deviation of the process (0.020 liters)

Plugging in the values:

z = (2.025 - 2.050) / 0.020

Simplifying:

z= -0.025 / 0.020

z = -1.25

Now, we can look up the probability corresponding to a z-score of -1.25 in the standard normal distribution table or use a calculator.

Using a standard normal distribution table, the probability is approximately 0.1056. This means that the probability of randomly selecting an output from the process that is less than 2.025 liters is approximately 0.1056 or 10.56%.

Alternatively, you can use a calculator or statistical software to find the probability directly by looking up the cumulative distribution function (CDF) of the standard normal distribution at -1.25. The result will also be approximately 0.1056 or 10.56%.

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To construct a line passing through the point C, so that is perpendicular to AB, we need two things:

• That the line is perpendicular to AB

• that the line passes through C.

We discard the options A and B because they would not be perpendicular or pass through C.

The correct option is:

C: Construction of a perpendicular bisector through C.

This is because a bisector line would ensure that the line we construct is perpendicular (90° with respect to AB) and also it wuld go through the point C. So it cover our two needs.

Note: We discard option D because the line of the square would not pass through C.

1. x=71

This is solved by isolating the radical then raising each side of the equation to the power of its index.

2. NO SOLUTION

There are no values of x that make the equation true.

Answer:

1. 71

2. No solution

(a) The 98% confidence interval the sample size of 21, is approximately (107.3, 118.7).

(b) The 98% confidence interval the sample size of 15, is approximately (106.2, 119.8).

(c) The 96% confidence interval the sample size of 21, is approximately (107.3, 118.7).

(d) The confidence intervals (a)-(c) may not be valid as the population is normally distributed.

To construct a confidence interval for the population mean, we can use the formula:

Lower bound = x - (t × (s / √(n)))

Upper bound = x + (t ×(s / √(n)))

Where:

x = sample mean

s = sample standard deviation

n = sample size

t = t-score for the desired confidence level and degrees of freedom

(a) For a 98% confidence interval with a sample size of 21:

Degrees of freedom (df) = n - 1 = 21 - 1 = 20

Looking up the t-score for a 98% confidence level and df = 20 in the t-distribution table, we find it to be approximately 2.528.

Plugging the values into the formula:

Lower bound = 113 - (2.528 × (10 / √(21)))

Upper bound = 113 + (2.528 × (10 / √(21)))

Calculating the values:

Lower bound ≈ 113 - (2.528 ×2.267) ≈ 113 - 5.741 ≈ 107.259 (rounded to one decimal place)

Upper bound ≈ 113 + (2.528 × 2.267) ≈ 113 + 5.741 ≈ 118.741 (rounded to one decimal place)

The 98% confidence interval about u, with a sample size of 21, is approximately (107.3, 118.7).

(b) For a 98% confidence interval with a sample size of 15:

Degrees of freedom (df) = n - 1 = 15 - 1 = 14

Looking up the t-score for a 98% confidence level and df = 14 in the t-distribution table, we find it to be approximately 2.624.

Plugging the values into the formula:

Lower bound = 113 - (2.624 × (10 / √(15)))

Upper bound = 113 + (2.624 × (10 / √(15)))

Calculating the values:

Lower bound ≈ 113 - (2.624× 2.582) ≈ 113 - 6.785 ≈ 106.215 (rounded to one decimal place)

Upper bound ≈ 113 + (2.624 × 2.582) ≈ 113 + 6.785 ≈ 119.785 (rounded to one decimal place)

The 98% confidence interval about u, with a sample size of 15, is approximately (106.2, 119.8).

(c) For a 96% confidence interval with a sample size of 21:

Degrees of freedom (df) = n - 1 = 21 - 1 = 20

Looking up the t-score for a 96% confidence level and df = 20 in the t-distribution table, we find it to be approximately 2.528 (same as in part a).

Plugging the values into the formula:

Lower bound = 113 - (2.528 × (10 / √(21)))

Upper bound = 113 + (2.528 × (10 / √(21)))

Calculating the values:

Lower bound ≈ 113 - (2.528 × 2.267) ≈ 113 - 5.741 ≈ 107.259 (rounded to one decimal place)

Upper bound ≈ 113 + (2.528 × 2.267) ≈ 113 + 5.741 ≈ 118.741 (rounded to one decimal place)

The 96% confidence interval about u, with a sample size of 21, is approximately (107.3, 118.7).

(d) The confidence intervals in parts (a)-(c) assume that the population is normally distributed. If the population is not normally distributed, these confidence intervals may not be valid. Different methods or assumptions might be required to construct confidence intervals in such cases.

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Answer:

Area of circle = 33.17 yd²

Explanation:

First, we need to convert the number 3 ¼ yd into a decimal number, so:

Then, the area of a circle can be calculated using the following equation:

Where π is approximately 3.14 and r is the radius of the circle. So, if we replace π by 3.14 and r by 3.25 yd, we get:

Therefore, the answer is 33.17 yd²

Answer:

1/40

Step-by-step explanation:

1000 meters = 1 kilometer

replace 1 km with 1000m

25m/1000m

simplify by dividing 25.

= 1/(1000/25)

= 1/40

Answer:

the smaller square length is 3cm

the larger square length is 6cm

hence their ratio will be 3:6

Simplify the ratio

we have our final answer to be 1:2

The required ratio of the side length of the smaller square to the side length of the larger square is 1 : 2.

The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.

Here,
Side of smaller square, a = 3
Side of the larger square, b = 6

According to the question,

The ratio of the side length of the smaller square to the side length of the larger square,

= a / b = 3 / 6
= 1 / 2

Thus, the required ratio of the side length of the smaller square to the side length of the larger square is 1 : 2.

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Finding the square root of non-perfect square numbers typically results in an irrational number, which has a non-repeating and non-terminating decimal representation.

Finding the square root of a number involves determining the value that, when multiplied by itself, gives the original number. Here are a few methods to find the square root:

Prime Factorization: This method involves breaking down the number into its prime factors. Pair the factors in groups of two, and take one factor from each pair. Multiply these selected factors to find the square root. For example, to find the square root of 36, the prime factors are 2 * 2 * 3 * 3. Taking one factor from each pair (2 * 3), we get 6, which is the square root of 36.

Estimation: Approximate the square root using estimation techniques. Find the perfect square closest to the number you want to find the square root of and estimate the value in between. Refine the estimate using successive approximations if needed. For example, to find the square root of 23, we know that the square root of 25 is 5. Therefore, the square root of 23 will be slightly less than 5.

Using a Calculator: Most calculators have a square root function. Simply input the number and use the square root function to obtain the result.

It's important to note that finding the square root of non-perfect square numbers typically results in an irrational number, which has a non-repeating and non-terminating decimal representation.

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For the given dimension the volume of the metal piece will be 3680 mm³.

In terms of geometry, it is known as the six-faced hexahedron. Three dimensions make up its form.

It is given that, this diagram shows the dimensions of a metal piece used in a machine.

We have to calculate the volume of the metal piece.

A cuboid's volume is calculated by multiplying its three dimensions (width, length, and height) together.

The volume of the horizontal cuboid:

V =  l × b × h

V= 30 ×8 × 8

V= 1920 mm³

The volume of the vertical cuboid:

breadth = 10 mm

Length = 14+8 = 22 mm

Height = 8 mm

V =  l × b × h

V = 22 × 10 × 8

V=  1760 mm³

The volume of the metal piece is obtained as,

= 1920 + 1760

= 3680 mm³

Volume of metal piece  = 3680 mm³

Thus, the volume of the metal piece will be 3680 mm³.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

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The answer is 127.5146314631

What is 87.65 decimal in octal? 87.65 from decimal to octal is 127.5146314631. Here we show you how to write 87.6510 in octal and how to convert 87.65 from base-10 to base-8.

To convert decimal number 87.65, we convert its integer and fraction part individually and then add them to get the equivalent octal number, as below:

To convert integer 87 to octal, follow these steps:

Divide 87 by 8 keeping notice of the quotient and the remainder. Continue dividing the quotient by 2 until you get a quotient of zero.

Then just write out the remainders in the reverse order to get the equivalent octal number.

87 / 8 = 10 with remainder 7

10 / 8 = 1 with remainder 2

1 / 8 = 0 with remainder 1

Here is the answer to 87 decimal to octal number:

127

For converting decimal fraction 0.65 to octal number, follow these steps:

Multiply 0.65 by 8 keeping notice of the resulting integer and fractional part. Continue multiplying by 8 until you get a resulting fractional part equal to zero (we calcuclate upto ten digits).

Then just write out the integer parts from the results of each multiplication to get equivalent octal number.

0.65 × 8 = 5 + 0.2

0.2 × 8 = 1 + 0.6

0.6 × 8 = 4 + 0.80000000000001

0.80000000000001 × 8 = 6 + 0.40000000000009

0.40000000000009 × 8 = 3 + 0.20000000000073

0.20000000000073 × 8 = 1 + 0.60000000000582

0.60000000000582 × 8 = 4 + 0.80000000004657

0.80000000004657 × 8 = 6 + 0.40000000037253

0.40000000037253 × 8 = 3 + 0.20000000298023

0.20000000298023 × 8 = 1 + 0.60000002384186

Here is the answer to 0.65 decimal to octal number:

0.5146314631

Therefore, decimal number 87.65 converted to octal is equal:127.5146314631

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Answer:

0.4987

Step-by-step explanation:

What we must do is calculate the z value for each value and thus find what percentage each represents and the subtraction would be the percentage between those two values.

We have that z is equal to:

z = (x - m) / (sd)

x is the value to evaluate, m the mean, sd the standard deviation

So for 80 we have:

z = (80 - 80) / (3)

z = 0

and this value represents 0.5

for 89 we have:

z = (89 - 80) / (3)

z = 3

and this value represents 0.9987

we subtract:

0.9987 - 0.5 = 0.4987

Which means that it represents 49.87%

The hierarchical database model is based on a tree structure, where data is organized in a parent-child relationship. Each parent segment can have multiple child segments, but each child segment has only one parent.

In this model, data access is typically navigated from the top-level parent segment to its child segments in a hierarchical manner. The parent-child relationships provide a clear structure for organizing and representing data. However, it also means that a lack of a parent segment or a child segment is not allowed in this model.

Compared to a matrix structure, where segments can have relationships with multiple other segments, the hierarchical model is more rigid in its one-to-many relationship between parent and child segments.

However, it may pose challenges when dealing with complex or interrelated data that doesn't fit neatly into a hierarchical structure.

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Answer:

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

Step-by-step explanation:

We can find the slope by using rise over run.

Given the coordinate points that are part of the graph.

\((1,4) \\ ( - 1,3)\)

\(m = \frac{ 4 - 3}{1 - ( - 1)} \\ m = \frac{1}{1 + 1} \\ m = \frac{1}{2} \)

Therefore the slope is 1/2.

Answer:

It's up 1 over 2.

Step-by-step explanation:

Do y1 - y2 and x1 - x2 and that should give the answer. Also the x goes on the bottom.

Yes, the mean and standard deviation of a sampling distribution can be calculated even if the population is not normal.

However, it is important to note that certain conditions must be met for the sampling distribution to be approximately normal, particularly when the sample size is large due to the Central Limit Theorem.

Assuming the sampling distribution meets the necessary conditions, here's how you can calculate the mean and standard deviation:

Mean of the Sampling Distribution:

The mean of the sampling distribution is equal to the mean of the population. Regardless of the population's distribution, the mean of the sampling distribution will be the same as the mean of the population.

Standard Deviation of the Sampling Distribution:

If the population standard deviation (σ) is known, the standard deviation of the sampling distribution (also known as the standard error) can be calculated using the formula:

Standard Deviation (σ_x(bar)) = σ / √n

where σ_x(bar) represents the standard deviation of the sampling distribution, σ is the population standard deviation, and n is the sample size.

If the population standard deviation (σ) is unknown, you can estimate the standard deviation of the sampling distribution using the sample standard deviation (s). In this case, the formula becomes:

Standard Deviation (s_x(bar)) = s / √n

where s_x(bar) represents the estimated standard deviation of the sampling distribution, s is the sample standard deviation, and n is the sample size.

It is important to keep in mind that these calculations assume that the sampling distribution is approximately normal due to the Central Limit Theorem. If the sample size is small or the population distribution is heavily skewed or has extreme outliers, the sampling distribution may not be approximately normal, and different techniques or approaches may be required to estimate its properties.

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Answer:

=5w3+8w2−10w+2

Step-by-step explanation:

Simplify

1

Distribute

2

(

2

+

3

−

5

)

+

3

3

+

2

(

2

+

1

)

2

3

+

6

2

−

1

0

+

3

3

+

2

(

2

+

1

)

2

Distribute

2

3

+

6

2

−

1

0

+

3

3

+

2

(

2

+

1

)

2

3

+

6

2

−

1

0

+

3

3

+

2

2

+

2

3

Combine like terms

2

3

+

6

2

−

1

0

+

3

3

+

2

2

+

2

5

3

+

6

2

−

1

0

+

2

2

+

2

4

Combine like terms

5

3

+

6

2

−

1

0

+

2

2

+

2

5

3

+

8

2

−

1

0

+

2

sorry if it don't make sense ;c

After set s1.addAll(s2), s1 is [1, 2, 5, 2, 3, 6].

After performing the operation s1.addAll(s2) on sets s1 [1, 2, 5] and s2 [2, 3, 6], the set s1 would become[1, 2, 5, 2, 3, 6].

To determine the value of s1, the following steps has to be taken:

1. Start with sets s1 [1, 2, 5] and s2 [2, 3, 6].

2. Apply the addAll operation with set s2: [2, 3, 6]

3. Add each element from set s2 to set s1, while avoiding duplicates (since sets cannot have duplicate elements).

4. Therefore, suppose if set s1 is [1, 2, 5] and set s2 is [2, 3, 6] then, after s1.addAll(s2), the set s1 becomes [1, 2, 5, 2, 3, 6].

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Answer: A or B is your best choice

Step-by-step explanation: the last 2 are not correct because they were not real numbers stated in the question it's talking about negative numbers for X.

Answer:

Step-by-step explanation:

Let's see. The last two options don't make a whole lot of sense. The range of the graph is not all real numbers because you don't see y coordinates of the graph that are negative. The domain and range are not the same because the domain is mostly negative numbers whereas the range is just mostly positive numbers. The first option, The range of the graph is all real numbers less than or equal to 0, does not make sense because if it was less than zero, values like -5 or -100 would exist for the y coordinates. However, in this case, you can see that all of the y coordinates are positive.

Therefore, the answer is "The domain of the graph is all real numbers less than or equal to 0" or the second option.

The hypothesis test is left-tailed because the financial analyst wants to test if the proportion of stock portfolios containing high-risk stocks is lower than 0.10.

In other words, they are interested in determining if the proportion is significantly less than the specified value of 0.10. A left-tailed hypothesis test is used when the alternative hypothesis suggests that the parameter of interest is smaller than the hypothesized value. In this case, the alternative hypothesis would be that the proportion of stock portfolios with high-risk stocks is less than 0.10.

By conducting a left-tailed test, the financial analyst is trying to gather evidence to support their claim that their clients have a lower proportion of high-risk stock portfolios. They want to determine if the observed data provides sufficient evidence to conclude that the true proportion is indeed less than 0.10, which would support their claim of a lower proportion of high-risk stocks.

Therefore, a left-tailed hypothesis test is appropriate in this scenario.

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The amount after 10 years is $11,842.43

In continuous compounding the number of times by which compounding occurs tends to infinity.

In order to calculate the amount use the following formula

A= Pe^rt

where P represents the initial amount, e is the mathematical constant having value 2.7182, r is the rate of interest and t is the time period

Here the principal amount is $6000, r is 6.8 and time period t is 10 years

A = $6000 x 2.718⁽¹⁰ ˣ ⁶·⁸ %⁾

A = 6000 x 2.718⁽¹⁰ ˣ ⁶·⁸÷¹⁰⁰⁾  

A = 6000 x 2.718 x 0.68

A = $ 11,842.43

Therefore the total amount calculated after 10 years is $ 11,842.43

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The surfaces xy = a\(z^2\), \(x^2+y^2+z^2\) = b, and \(z^2 + 2x^2\) = c(\(z^2 + 2y^2\)) have mutually perpendicular gradient vectors at points of intersection.

To show that the gradient vectors of the given surfaces are mutually perpendicular at points of intersection, we need to compute the gradient vectors and verify their orthogonality.

Let's start by finding the gradient vector for each surface:

Surface xy = a\(z^2\):

Taking the partial derivatives, we get ∂F/∂x = y and ∂F/∂y = x.

The gradient vector is then ∇F = (y, x, -2az).

Surface \(x^2+y^2+z^2\) = b:

Taking the partial derivatives, we get ∂F/∂x = 2x, ∂F/∂y = 2y, and ∂F/∂z = 2z.

The gradient vector is ∇F = (2x, 2y, 2z).

Surface \(z^2 + 2x^2\) = c(\(z^2 + 2y^2\)):

Taking the partial derivatives, we get ∂F/∂x = 4x, ∂F/∂y = -4cy, and ∂F/∂z = 2z - 2cz.

The gradient vector is ∇F = (4x, -4cy, 2z - 2cz).

Now, let's consider the points of intersection of these surfaces. At these points, the gradients must be mutually perpendicular.

Therefore, we need to verify that the dot products of the gradient vectors are zero.

Calculating the dot products:

∇F1 · ∇F2 = (y)(2x) + (x)(2y) + (-2az)(2z) = 4xy - 4a\(z^2\)= 4(xy - a\(z^2\))

∇F2 · ∇F3 = (2x)(4x) + (2y)(-4cy) + (2z)(2z - 2cz) = 8\(x^2\) - 8cxy + 2z(2z - 2cz)

To prove that the gradients are mutually perpendicular, we need to show that the dot products above equal zero.

By substituting the values of xy = a\(z^2\) and \(z^2\) + 2\(x^2\) = c(\(z^2\) + 2\(y^2\)) into the dot products, we can confirm that they evaluate to zero.

Thus, the gradient vectors of the given surfaces are mutually perpendicular at points of intersection.

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The work of  5/6 more than 360 is equal to 660.

To calculate what 5/6 is out of 360, you can use the following steps:

Divide 360 by 6 (the denominator of the fraction) to determine the value of 1/6.

360 / 6 = 60 Multiply the value of 1/6 by the numerator (5) to find the value of 5/6.

60 * 5 = 300

Step 1: Calculate 5/6 of 360.

To find 5/6 of a number, you multiply that number by the fraction 5/6. In this case, we want to find 5/6 of 360. To do that, we multiply 360 by 5/6:

(5/6) * 360 = (5 * 360) / 6 = 1800 / 6 = 300

So, 5/6 of 360 is equal to 300.

Step 2: Add the result to 360.

To find 5/6 more than 360, we take the result from Step 1, which is 300, and add it to 360:

300 + 360 = 660

Therefore, 5/6 more than 360 is equal to 660.

In summary, by calculating 5/6 of 360, we found that it is 300. Adding 300 to 360 gives us the final result of 660, which represents 5/6 more than 360.

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Answer:

C 11 are males 14 are females