what is the measure of angle a?

Answer: 160

Step-by-step explanation:

Answer:

160

Step-by-step explanation:

Let 100 = 5 in the ratio of 8:5

100/5 = 20 per piece of the ratio

Times both sides by 20 for new value:

8:5 x 20 = 160:100

Answer = 160

From the data points given the linear equation in slope-intercept form is y = -1/2x + 4.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The first two data points are - (-3,5.5) and (-1,4.5)

The slope-intercept form of the equation is -

y = mx + b

m represents the slope of the linear equation.

To find the value of m use the formula -

(y2 - y1)/(x2 - x1)

Substitute the values into the equation -

(4.5 - 5.5)/[(-1) - (-3)]

Use the arithmetic operation of subtraction -

(-1)/(-1 + 3)

-1 / 2

So, the slope m is m = -1/2

Now, the equation becomes y = -1/2x + b

To find the value of b substitute the  values of x and y in the equation -

5.5 = -1/2(-3) + b

5.5 = 3/2 + b

5.5 = 1.5 + b

b = 5.5 - 1.5

b = 4

So, now the equation becomes - y = -1/2x + 4

The graph for the equation is plotted.

Therefore, the equation is y = -1/2x + 4.

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Answer:

1/6 or 0.16...

Step-by-step explanation:

Approximately 601 asthmatic patients would need to be included in the study to estimate the true percentage within a 4% margin of error and a 95% confidence interval.

The given information provides a 95% confidence interval for the true percentage of asthmatic patients who experience breathing difficulties after taking benzalkonium chloride (BAC).

However, there are certain factors that can lead to erroneous inferences based on this confidence interval.

The confidence interval may lead to an erroneous inference due to the following reasons:

Small sample size: The sample size of 18 asthmatic patients is relatively small.

With a small sample, there is a higher chance of sampling variability, which may affect the accuracy of the confidence interval. A larger sample size would provide more reliable estimates.

Non-representative sample: The sample of asthmatic patients may not be representative of the entire population of asthmatic patients.

If the sample is not representative, the confidence interval may not accurately reflect the true percentage of patients who experience breathing difficulties after taking BAC.

Potential biases: There may be biases in the sample selection process or in the measurement of breathing difficulties.

Biases can introduce systematic errors that affect the validity of the confidence interval.

To estimate the true percentage of asthmatic patients who experience a significant drop in breathing capacity to within 4% with a 95% confidence interval, we need to determine the required sample size.

The formula to calculate the sample size for estimating proportions is n = (\(Z^2\) × p × q) / (\(E^2\)), where Z is the z-score corresponding to the desired confidence level, p is the estimated proportion, q is 1-p, and E is the desired margin of error.

In this case, we want a 95% confidence interval and a margin of error of 4%, so the z-score corresponding to a 95% confidence level is approximately 1.96.

The estimated proportion can be taken as 0.5 (assuming the worst-case scenario where the true proportion is 50%).

Plugging these values into the formula, we get:

n = (\((1.96)^2\) × 0.5 × 0.5) / (\((0.04)^2\)) ≈ 600.25

Therefore, approximately 601 asthmatic patients would need to be included in the study to estimate the true percentage within a 4% margin of error and a 95% confidence interval.

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The recursive formula that represents the same sequence of numbers as the explicit formula an = 3n + 4 is an = an-1 + 3, with the initial term a1 = 7.

A recursive formula defines a sequence by expressing each term in terms of previous terms. In this case, the explicit formula an = 3n + 4 gives us a direct expression for each term in the sequence.

To find the corresponding recursive formula, we need to express each term in terms of the previous term(s). In this sequence, each term is obtained by adding 3 to the previous term. Therefore, the recursive formula is an = an-1 + 3.

To complete the recursive formula, we also need to specify the initial term, a1. We can find the value of a1 by substituting n = 1 into the explicit formula:

a1 = 3(1) + 4 = 7

Hence, the complete recursive formula for the sequence is an = an-1 + 3, with the initial term a1 = 7. This recursive formula will generate the same sequence of numbers as the given explicit formula.

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The sample standard deviation is approximately 0.83.

Sample size \(($n$)\) = 36

Population mean \(($\mu$)\) = 50

Population standard deviation \(($\sigma$)\) = 5

The sample standard deviation, denoted as \($s$\) can be estimated using the formula:

\(\[ s = \sqrt{\frac{\sum_{i=1}^{n}(x_i - \bar{x})^2}{n-1}} \]\)

where:

\($x_i$\) represents the individual data points in the sample

\($\bar{x}$\) is the sample mean

In this case, since we don't have individual data points, we can use the population standard deviation as an estimate for the sample standard deviation when the sample size is relatively large (as in this case \($n = 36$\)). This approximation is known as the standard error of the mean.

Therefore, the sample standard deviation can be approximated as:

\(\[ s \approx \frac{\sigma}{\sqrt{n}} \]\)

Substituting the given values:

\(\[ s \approx \frac{5}{\sqrt{36}} = \frac{5}{6} \] = 0.83\)

Hence, the sample standard deviation is approximately 0.83.

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An 18-year-old male being between 65 and 67 inches tall at random has a probability of about 0.3830. The likelihood that the mean height of a sample of twenty-nine men aged 18 falls between 65 and 67 inches is higher when taking into account. This is due to the fact that as sample size grows, the standard deviation drops, leading to a narrower distribution of sample means.

(1) We need to determine the area under the normal distribution curve between these two numbers in order to determine the likelihood that a randomly chosen 18-year-old guy will be between 65 and 67 inches tall. The formula for calculating z-score is z = (x - ) / z, where x is the measurement we are interested in (in this case, 65 and 67 inches), is the mean (66 inches), and is the standard deviation (4 inches).

Making a z-score calculation for 65 and 67 inches:

z1 = (65 - 66) / 4 = -0.25 z2 = (67 - 66) / 4 = 0.25

We may calculate the region between these z-scores using a calculator or a conventional normal distribution table. The area is roughly 0.5987 square metres. But because we're interested in the likelihood that the length will be between 65 and 67 inches, we deduct the left tail area from the right tail area:

Probability = 0.5987 - 0.4013 = 0.1974 (rounded to four decimal places to equal about 0.3830).

(2) The Central Limit Theorem asserts that, regardless of the shape of the initial population, the distribution of sample means becomes roughly normally distributed when the sample size is big. This is true when evaluating the mean height of a sample of twenty-nine 18-year-old men. In this situation, we can suppose that the sample size of 29 is sufficient for the approximation.

The population mean (x), which is 66 inches, is the same as the mean of the sample means (x). The population standard deviation () divided by the square root of the sample size (n) yields the standard deviation of the sample means (x), commonly referred to as the standard error of the mean.

(Rounded to four decimal places) x = n / 4 / 29 = 0.7435.

We can calculate the z-scores using the same formula as in section (1) to determine the likelihood that the mean height falls between 65 and 67 inches.

z1 = (65 - 66) / 0.7435 ≈ -1.3441

z2 = (67 - 66) / 0.7435 ≈ 1.3441

The area between these z-scores, according to a calculator or a normal distribution table, is roughly 0.8784. As a result, the likelihood that the mean height for a sample of 29 men aged 18 falls between 65 and 67 inches is roughly 0.8784 (rounded to four decimal places).

(3) Because the sample means distribution's standard deviation (x) is lower than that of the initial population distribution, the probability in part (2) is higher. The standard deviation of the sample means falls as sample size rises. Due to the narrower distribution of sample means produced by the reduced variability, it is more probable that the sample mean will fall inside a particular range. With a suitable sample size, the sample means will be more closely clustered around the population mean, improving the likelihood of finding a mean within a specified interval, according to the Central Limit Theorem. As a result of the sample means distribution's smaller standard deviation, the probability in part (2) is significantly larger.

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Answer:

Step-by-step explanation:

You want the zeros of f(x) = x³ -5x² -22x -16, given that a factor is x+2.

Using synthetic division (see attachment), we find the quadratic factor to be (x² -7x -8), so we have ...

  f(x) = (x +2)(x² -7x -8)

The quadratic can be factored using our knowledge of the divisors of -8 to give ...

  f(x) = (x +2)(x +1)(x -8)

The zeros of f(x) are the values of x that make these factors zero:

  x = -2, -1, 8 . . . . . zeros of f(x)

__

Additional comment

We know the product of binomial factors is ...

  (x -a)(x +b) = x² -(a-b)x -ab

This means we can factor the quadratic by looking for factors of 8 that have a difference of 7. We know that 8 = 8·1 and that 8-1=7, so the values of 'a' and 'b' we're looking for are a=8, b=1.

The "zero product rule" tells you a product is zero only if one of the factors is zero. That is how we know to look for the zeros of the binomial factors of f(x). For example, x+2=0 ⇒ x=-2 is a zero of f(x). (The remainder of 0 in the synthetic division also tells us f(-2)=0.)

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Answer:

You can't find the area or perimeter with the information given. If this is a calculus level problem then it is possible.

The expressions are expanded to give;

1. 2x² - 5x

2. 6x² + 8x

3. 6x² - 12xy

Algebraic expressions are defined as expressions consisting of  variables, coefficients, constants, terms and factors.

These expressions are also known to consist of mathematical operations, which includes;

From the information given, we have that;

a. x (2x - 5)

expand the bracket

2x² - 5x

b. 2x (3x+4)

expand the bracket

6x² + 8x

c. 6x(x-2y)

expand the bracket

6x² - 12xy

Hence, the expressions are 2x² - 5x, 6x² + 8x and 6x² - 12xy

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Answer:

1) 2x² - 5x

2) 6x² + 8x

3) 6x² - 12xy

Step-by-step explanation:

1) x ( 2x - 5 )

To expand the above, multiply both terms inside the brackets by x.

2x² - 5x

2) 2x ( 3x + 4 )

To expand the above, multiply both terms inside the brackets by 2x.

6x² + 8x

3) 6x ( x - 2y )

To expand the above, multiply both terms inside the brackets by 6x.

6x² - 12xy

For a survey of community related to build a police substation in their nearby, from binomial distribution the probability that the number favoring the substation is more than 12 is 0.398.

We have a survey related to community view regarding building a police substation in their nearby. Let X be an event for favouring the building a police substation in their nearby. The

Probability of community favored building a police substation in their neighborhood = 80% = 0.80

Total number of selected citizens = 15

We have to determine the probability that the number favoring the substation is more than 12. Using Binomial probability distribution, P( X = x) = ⁿCₓ pˣ( 1- p)⁽ⁿ⁻ˣ⁾

where, p --> probability of success

x -> number of success

n -> total number of trials

here, n = 15, p = 0.80, x = 12, substitute all known values in above formula, P( X >12) = P( X= 13) + P( X = 14) + P(X = 15)

= ¹⁵C₁₃ 0.8¹³(0.2)² + ¹⁵C₁₄ 0.8¹⁴(0.2)¹ + ¹⁵C₁₅0.8¹⁵ 0.2⁰

= 0.231 + 0.132 +0.035

= 0.398

Hence, the required probability is 0.398.

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The equation of the line of best fit is y=1.797x+0.904

From the question n=5,

\(\quad \sum x=42, \sum y=80, \sum x^2=478, \sum x y=897 \\& \therefore \quad \bar{x}=\frac{\sum x}{n}=\frac{42}{5}=8.4= \\& \bar{y}=\frac{\sum y}{n}=\frac{80}{5}=16 \\$ \end\)

\(\\& \sigma_x^2=\frac{\sum x^2}{n}-\bar{x}^2=\frac{478}{5}-8.4^2=25.04 \\\)

\(& \ {cov} (x, y)=\frac{\sum x y}{n}-\bar{x} \bar{y}=\frac{897}{5}\)-8.4*16=45

Now, The slope of the regression equation is,

\($b=\frac{\ {cov}(x, y)}{\sigma_x^2}\)

=\(\frac{45}{25.04}\)=1.797

The intercept of the regression equation is,

a=-b=16-1.797*8.4=0.904

The equation for the line of best fit for the following data is,

y=bx + a

[c]y=1.797x+0.904

The equation of the line is y=mx+c

Therefore, the equation of the line of best fit for the following data is 1.797x+0.904

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Answer:

0.17391304347

Step-by-step explanation:

There is multiple names it has, like for example “Zero” and in British English it is “nought” which is often used as an archaic word for nothing, I hope this help’s.

The mean delivery time for a random sample of 16 orders is 7.7 minutes, and the standard deviation of the sample mean is 0.525 minutes. The shape of the sampling distribution of x is approximately normal.

The mean delivery time for a random sample of 16 orders can be calculated using the formula for the mean of a sampling distribution:

Mean of x = Mean of population = 7.7 minutes

The standard deviation of x can be calculated using the formula for the standard deviation of a sampling distribution:

Standard deviation of x = Standard deviation of population / sqrt(sample size)

= 2.1 minutes / √(16)

= 2.1 minutes / 4

= 0.525 minutes

The shape of the sampling distribution of x is approximately normal. According to the Central Limit Theorem, for a sufficiently large sample size (n > 30), the sampling distribution of the sample mean tends to be approximately normally distributed regardless of the shape of the population distribution.

In this case, the sample size is 16, which is smaller than 30. However, since the population distribution is assumed to be normal, the sampling distribution of the sample mean will still be approximately normal due to the normality of the population distribution.

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Step-by-step explanation:

slope of the segment through (-9, -8) and (-5, 6) is (-9-(-5))/(-8-6)=-(-4)/(-14)=2/7

this means the slope of the perpendicular is -7/2.

the midpoint of the segment is (-7, -1)

so the line is y+1=(-7/2)(x+7).

A "required parameter" requires an assigned value for the argument used to call the method, while "optional parameters" do not need to be included in the method call and have a default value assigned to them.

The type of parameter that requires that the argument used to call the method must have an assigned value is a "required parameter".

Required parameters are parameters that must be included in the method call, and the argument passed for the required parameter must have a value assigned to it. If a required parameter is not included in the method call, or if the argument passed for the required parameter does not have a value assigned to it, an error will be thrown.

In contrast, there are also optional parameters, which are parameters that do not need to be included in the method call. If an optional parameter is not included in the method call, the method will use a default value assigned to the parameter.

In many programming languages, the syntax for specifying required and optional parameters in a method or function call is specified using different symbols, such as parentheses or square brackets.

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The solution to the equation given as 4(3x + 4) = 4x + 8 is x =-1

Expressions are mathematical statements that are represented by variables, coefficients and operators

The equation is given as

4(3x + 4) = 4x + 8

Open the bracket in the above equation

So, we have

12x + 16 = 4x + 8

Collect the like terms in the above equation

12x - 4x = 8 - 16

Evaluate the like terms in the above equation

8x = -8

Divide both sides by 8 in the above equation

x =-1

Hence, the solution to the equation given as 4(3x + 4) = 4x + 8 is x =-1

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A good example of notation is musical notation. This kind of notation system can be used by a composer to instruct performers and listeners on how to play and hear their music. There are many different types of symbols and pictures in it.

Assuming you want to write this expression in mathematical notation, you can use the variable J to represent the total number of items being divided into three equal groups, and write the expression as:

(J/3) + 2

Here, (J/3) represents the number of items in each of the three equal groups, and adding 2 to this quantity gives the total number of items when 2 more are added to each group.

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The expression would be (J/3) + 2.

What is an expression?

In mathematics, an expression is a combination of one or more numbers, variables, and operators, typically arranged according to the rules of algebra, that represents a value or a quantity. Expressions can be as simple as a single variable or number, or they can be complex, involving multiple variables, functions, and operators.

If we represent "J" as a number, we can write this expression as:

(J/3) + 2

This represents the result of dividing "J" into three equal groups and then adding 2 more.

Hence, the expression would be (J/3) + 2

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Answer:

BHN is the name of angle

Step-by-step explanation:

Answer:

In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

Step-by-step explanation:

With employees ranging in age from 40 to 30, 36 to 22, there is a 46-year age difference between them. The average difference between each age and the population's mean age is measured.

We employ the following formula to determine the variance of a population:

σ² = Σ(x - μ)² / N

σ² = Σ(x - μ)² / N

where:

σ² =  the population variance

Σ = the sum of

x = the value of each element in the population

μ = the population mean

N = the population size

First, we need to find the population mean:

μ = (40 + 30 + 36 + 22) / 4 = 32

Next, we calculate the sum of the squared deviations from the mean:

(40 - 32)² + (30 - 32)² + (36 - 32)² + (22 - 32)² = 64 + 4 + 16 + 100 = 184

Then, we divide the sum of squared deviations by the population size:

σ² = Σ(x - μ)² / N = 184 / 4 = 46

Therefore, the population variance is 46.

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Answer:

76

Step-by-step explanation:

total=180

180-104=76

Answer:

(a) Brief Solution: The null hypothesis (H0) is that the average weight loss of newborn babies in the hospital is equal to 7 ounces, while the alternative hypothesis (H1) is that the average weight loss is less than 7 ounces. The obstetrician's claim supports the alternative hypothesis.

Step-by-step explanation:

The null hypothesis (H0) assumes that there is no significant difference between the average weight loss of newborn babies in the hospital and 7 ounces. The alternative hypothesis (H1) suggests that there is a difference, specifically a lower weight loss.

To determine if there is enough evidence to support the obstetrician's claim, we can perform a one-sample t-test. Since the population standard deviation is known (1.3 ounces) and the sample size is 35, we can use the critical value method. By comparing the calculated test statistic (t-value) with the critical value from the t-distribution table at a significance level of 0.01, we can make a decision on whether to reject the null hypothesis or not.

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Answer:

30

Step-by-step explanation:

To find this out we are going to use PEMDAS.

What is PEMDAS? P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition, and S- Subtraction.

For this we are going to divide first as multiplication and division do not matter on which one you use first.

So 18/3 is going to be 6.

Then we are going to multiply.

So 6 x 4  is going to be 24.

Last we are going to add them together.

24 + 6 is going to be 30.

So your anwser is going to be 30.

Answer:

9.919742348374221

Step-by-step explanation:

(x+5)(x)=x^2+5x. (x^2+5x)/2; x=

9.919742348374221