Given the triangle below...
30°
B
79
A
What is the measure of angle B?

We can use a normal probability model to represent the distribution of sample means when the sample size is large enough to ensure that sample means will be normally distributed, option (C) is correct.

The central limit theorem (CLT) states that when sample sizes are sufficiently large (typically, n > 30), the distribution of sample means will be approximately normal, regardless of the distribution of the variable in the population.

This is because as the probability of sample size increases, the sample mean becomes a more reliable estimate of the population mean, and the variability in the sample means decreases. This results in a distribution that is bell-shaped and symmetric, similar to a normal distribution, option (C) is correct.

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– The question is inappropriate, The correct question is:

We can use a normal probability model to represent the distribution of sample means for which of the following reasons? check all that apply.

A) the sample is randomly selected

B) the distribution of the variable in the population is normally distributed

C) the sample size is large enough to ensure that sample means will be normally distributed flag –

Answer:

Y= (x+4)(x+4)-21

Step-by-step explanation:

If you are factoring It out:

Y=-2x^2+8x-5 is the same as Y= (x+4)(x+4)-21

Let me know if it is incorrect!

-a friendly 8th grader

The equation of the line CD obtained from the slope of the line AB, and the coordinates of the point C is; 7·y - 3·x = 2

The slope of a line is the ratio of the rise to the run of the line.

The specified information indicates;

AB ║ CD

The coordinates of the point A is (-3, 2), the coordinates of the point B is (4, 5)

The slope of the segment AB is therefore; (5 - 2)/(4 - (-3)) = 3/7

The coordinates of the point C is; (4 , 5 - 3) = (4, 2)

The equation of the line CD is therefore; y - 2 = (3/7)·(x - 4)

7·y - 14 = 3·x - 12

7·y - 3·x = 14 - 12 = 2

The equation of the segment CD is; 7·y - 3·x = 2

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The value of x is given as follows:

x = 2.25.

The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.

From the image at the end of the answer, we have that 3 is the geometric mean of 4 and x, hence the value of x is obtained as follows:

4x = 3²

4x = 9

x = 9/4

x = 2.25.

The image is given at the end of the answer.

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For the data set 29, 20, 15, 13, 35, 20. the mean, median, mode and range are 22, 20, 20, and 22, respectively.

The mean (arithmetic mean), denoted by μ, is a single value defined as the sum of the data values divided by the total number of data values.

[tex]\text{Mean} =\dfrac{x_1+x_2+...+x_n}{\text{N}}[/tex]

[tex]\text{Mean} = \dfrac{29+20+15+13+35+20}{6}[/tex]

[tex]\text{Mean} = 22[/tex]

The median, denoted by , is the single value at the middle of an ordered arrangement of data values according to increasing or decreasing magnitude.

[tex]\text{M}_{\text{d}}=x_{\dfrac{\text{N}+1}{2} }[/tex]     if N is odd, and

[tex]\text{M}_{\text{d}}=\dfrac{^x\frac{\text{N}}{2}^{+x} \frac{\text{N}}{2} +1}{y}[/tex]    if N is even

[tex]\text{N = 8}[/tex]

Data : 13, 15, 20, 20, 29, 35

[tex]\text{M}_{\text{d}}=\dfrac{^x\frac{\text{N}}{2}^{+x} \frac{\text{N}}{2} +1}{y}[/tex]

where [tex]x_\frac{\text{N}}{2}[/tex] = [tex]x_\frac{8}{2}[/tex] = [tex]x_4[/tex] = 20 and [tex]x_\frac{\text{N}}{2}_{+1}=x_\frac{8}{2}_{+1}=x_4_{+1}=x^5[/tex] = 20

[tex]\text{M}_{\text{d}}=\dfrac{20+20}{2}[/tex]

[tex]\text{M}_{\text{d}}=20[/tex]

The mode, denoted by , refers to the most frequent value in the data set.

[tex]\text{Mode = 20}[/tex]

The range (R) is defined as the difference between the maximum and minimum values of a data set.

[tex]\text{R} = \text{MAX} - \text{MIN}[/tex]

[tex]\text{R} = 35- 13[/tex]

[tex]\text{R} = 22[/tex]

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Answer:

8/27.

Step-by-step explanation:

To find out which class had the greatest fraction of students who preferred vanilla ice cream, we need to compare the ratios of students who preferred vanilla to the total number of students in each class.

For second period class:

Number of students who preferred vanilla = 725

Total number of students = unknown

Ratio of students who preferred vanilla to total number of students = unknown/unknown = undefined

For fourth period class:

Number of students who preferred vanilla = 8

Total number of students = 27

Ratio of students who preferred vanilla to total number of students = 8/27

For sixth period class:

Number of students who preferred vanilla = 30% of total number of students

Total number of students = unknown

Ratio of students who preferred vanilla to total number of students = 0.3*unknown/unknown = 0.3

Therefore, the fourth period class had the greatest fraction of students who preferred vanilla ice cream, with a ratio of 8/27.

Kendrick's basil plant is now 6 inches tall.

If the basil plant was originally 4 inches tall and grew to a height of 1 foot (12 inches), then its total growth is 12 - 4 = 8 inches.

If Kendrick then cuts off 6 inches from the plant, the new height of the plant is 12 - 6 = 6 inches.

Therefore, Kendrick's basil plant is now 6 inches tall.

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The value of y for the inverse variation when x = -3 is derived to be equal to -8, and the equation that relating x and y is: y = 24/x.

Inverse variation is a mathematical relationship between two variables, in which an increase in one variable leads to a proportional decrease in the other variable. Mathematically, inverse variation can be expressed as y = k/x, where y and x are the two variables, k is a constant of proportionality, and the product of y and x is always equal to k.

when x = -4 and y = -6, then k is derived as:

-6 = k/-4

k = 24 {cross multiplication}

equation relating x and y is:

y = 24/x

when x = -3, y is derived as:

y = 24/-3

y = -8

Therefore, the value of y for the inverse variation when x = -3 is derived to be equal to -8, and the equation that relating x and y is: y = 24/x.

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They have traveled 234 miles when they completed 72 percent of the trips distance ​

from the question, we have the following parameters that can be used in our computation:

Distance = 325 miles

Distance completed = 72%

Using the above as a guide, we have the following:

Distance completed = 72% * Total distance

Substitute the known values in the above equation, so, we have the following representation

Distance completed = 72% * 325 miles

Evaluate

Distance completed = 234 miles

Hence, the distance completed = 234 miles

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Answer:

To perform McNemar's test, we need to find the number of discordant pairs, i.e., the pairs of individuals who change their response from before to after college. In this case, there are 23 students who said "yes" before college but "no" after college, and 11 students who said "no" before college but "yes" after college. Therefore, there are 23 discordant pairs.

The test statistic for McNemar's test is calculated as:

z = (|b-c| - 1) / √(b+c)

where b is the number of discordant pairs who responded "yes" before college, and c is the number of discordant pairs who responded "no" before college.

In this case, b = 23 and c = 11, so:

z = (|23-11| - 1) / √(23+11)

z = 1.96

Therefore, the test statistic is 1.96

Answer:

32.5

Step-by-step explanation:

hope this helps

Answer: (7, 1)

Step-by-step explanation:

To find the coordinates of Q' which is the image of point Q(0, 6) under the translation (x, y) → (x + 7, y − 5), we can apply the translation to the coordinates of Q as follows:

x-coordinate of Q' = x-coordinate of Q + 7

= 0 + 7

= 7

y-coordinate of Q' = y-coordinate of Q - 5

= 6 - 5

= 1

Therefore, the coordinates of Q' are (7, 1).

For the function f to be linear, the number that should be written in the penultimate line of the script should be 0 because a linear function has a constant slope and no term with a power higher than 1.

In the general form of a linear function

y = mx + b

where m is the slope and b is the y-intercept.

Since the function f is defined as

f(x) = x² + mx + b

we can see that it is a quadratic function.

Therefore, to make it linear, we need to eliminate the x² term.

To eliminate the x² term, we can set the coefficient of x² to 0. Since the coefficient of x² is 1, we can subtract x² from both sides of the equation

f(x) = x² + mx + b

f(x) - x² = mx + b

Now, we have a linear function since the term with x² has been eliminated. Thus, the number that should be written in the penultimate line of the script is 0, which will make the coefficient of x² equal to 0 and eliminate the quadratic term.

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Getting married in December and filing a joint return would result in a lower tax liability by: $65,917.

Based on the given tax schedules, if Leni and Thom get married in December and file a joint return, their total tax liability would be:

$4,220 for the first $19,900 of taxable income

$20,227 for the remaining $210,100 of taxable income ($230,000 - $19,900)

Total tax liability: $24,447

If they get married in January of the next year and file separate returns, each as a single taxpayer, their total tax liability would be:

Leni's tax liability: $45,182

Thom's tax liability: $45,182

Total tax liability: $90,364

Therefore, getting married in December and filing a joint return would result in a lower tax liability by: $90,364 - $24,447 = $65,917.

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In the given triangle IJK, the measure of angle J is approximately 32°

From the question, we are to determine the measure of angle J in the given triangle

From the Law of Sines,

We can write that

sin (I) / i = sin (J) / j

From the given information,

j = 530 cm

i = 740 cm

∠I = 133°

Substituting the parameters into the formula,

sin (I) / i = sin (J) / j

sin (133°) / 740 = sin (J) / 530

sin (J) = (530 × sin (133°)) / 740

sin (J) = 0.5238

J = sin⁻¹ (0.5238)

J = 31.59°

J ≈ 32° (to the nearest degree)

Hence,

The measure of angle J is approximately 32°

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Answer:

B. It is not a function.

This graph is a circle.

Kira will be paid $120 in interest in the first two years.

Simple interest is expressed as;

I = P × r × t

Where I is the interest, P is the principal amount, r is the interest rate per year, and t is the time in years.

Given that:

Substituting the given values, we get:

I = P × r × t

I = 2000 × 0.03 × 2

I = $120

Therefore, the interest in the first two years is $120.

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if you swim diagonally across the pool, you would be swimming for 15 meters.

A rectangle is a 2-dimensional shape with four straight sides and four right angles. It is a type of quadrilateral where opposite sides are parallel and congruent, and all angles are 90 degrees (right angles). The length of a rectangle is typically defined as the longer side, and the width is the shorter side.  

We can use the Pythagorean theorem to find the length of the diagonal:

diagonal² = width² + length²

Substituting the given values, we get:

diagonal² = 9² + 12²

diagonal² = 81 + 144

diagonal² = 225

diagonal = √(225)

diagonal = 15 meters

Therefore, if you swim diagonally across the pool, you would be swimming for 15 meters.

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Retained earnings, December 31, 2018                               $6,470,000

Add: Net income December 31, 2019                                  $4,500,000

Less: Preferred stock dividends declared and paid           $4,500,000

Less: Common stock dividends declared and paid            $1,000,000

Total adjustments                                                                  $3,500,000

Retained earnings, December 31, 2019                             $9,970,000

The statement shows changes in the balance of retained earnings account during the year. The retained earnings balance at the beginning of the year is adjusted for the net income earned during the year and for the dividends declared and paid to the shareholders.

In this case:

So, total adjustments to the retained earnings balance:

= $4,500,000 + $1,000,000 - $4,500,000.

= $3,500,000

After adjustment on net income and dividends, the retained earnings balance at December 31 2019 is:

= $6,470,000 + $4,500,000 - $3,500,000

= $9,970,000

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Answer: The answer to

sinΘ = 7/7√2

cosΘ = 7/7√2

tanΘ = 7/7

cosecΘ = 7√2/7

secΘ = 7√2/7

cotΘ = 7/7

Step-by-step explanation:

The given triangle consists of three sides namely, hypotenuse, opposite and adjacent.

The value of the hypotenuse is 7√2 and the value of the adjacent is 7.

We will calculate the value of the adjacent.

By Pythagoras' theorem,  (hypotenuse)^2=(opposite)^2+(adjacent)^2

Putting the given values, (7√2)^2=(opposite)^2+(7)^2

                                         (opposite)^2=(7√2)^2-(7)^2

                                         (opposite)^2=98-49

                                         (opposite)^2=49

Therefore, the value of the opposite is 7.

Now, we can put the following values in the trigonometric table.

sinΘ = opposite/hypotenuse = 7/7√2

cosΘ = adjacent/hypotenuse = 7/7√2

tanΘ =  opposite/adjacent = 7/7

cosecΘ = hypotenuse/opposite = 7√2/7

secΘ = hypotenuse/adjacent = 7√2/7

cotΘ = adjacent/opposite = 7/7

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1. $0.5 is 1/2 of a dollar

2. The fraction of her times at a bat that she get a hit is 1/4

Decimals are the numbers, which consist of two parts namely, a whole number part and a fractional part separated by a decimal point.

For example, 0.4 is 0 + 4/10 = 4/10,/. This means the conversion of 0.4 to fraction is 4/10.

1. The fraction of $0.5 to $1 is calculated as;

representing the fraction by x

x of 1 = 0.5

0.5 = 5/10

therefore

x= 5/10 = 1/2

Therefore the fraction of $1 that gives $0.5 is 1/2

2. converting 0.250 to fraction

= 0 + 250/1000

= 250/1000

= 25/100 = 5/20 = 1/4

therefore the fraction of Sue's hit is 1/4.

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The value of cos (2theta) will be; 161/289

We are given that tan(A) = -8/15, therefore opposite is 8 and adj is 15

hyp = √8²+15²

= √ 64+225

= √ 289

= 17

Thus, cos (theta) = 8/17 and since theta is in second quadrant, cos tetha will be negative

cos (theta) = -15/17

cos²(theta) = 225/289

sin(theta) = 8/17

sin²(theta) = 64/289

cos(2theta) = cos²(theta) -sin²(theta)

= 225/289 - 64/289

= 161/289

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The binomial probability model is useful in situations with discrete-valued numerical variables. Hence, the answer is option (a) discrete-valued numerical variables.

The binomial distribution is a probability model that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (e.g., success or failure, heads or tails, etc.).

The binomial distribution can be used to model a wide range of real-world scenarios, such as the number of defective products in a batch of goods, the number of heads in a series of coin flips, or the number of people who respond positively to a survey question.

Therefore, the correct option is (a)  discrete-valued numerical variables.

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The total quantity produced when p = 5 is 26 in the long run.

In the short run, each firm will produce where its marginal cost equals the market price, which we'll denote as p.

So, for Type A firms, the short-run supply curve is:

q4(p) = (p-2)/2

And for Type B firms, the short-run supply curve is:

qB(p) = (p-2)/6

The short-run market supply is simply the sum of the quantities supplied by each type of firm at a given price level. So, if there are 10 Type A firms and 6 Type B firms, the short-run market supply at a price level of p is:

Qs(p) = 10q4(p) + 6qB(p)

= 10(p-2)/2 + 6(p-2)/6

= 8p - 20

The total quantity produced when p=5, we can substitute p=5 into the market supply equation we just derived:

Qs(5) = 8(5) - 20

= 20

So, the total quantity produced when p=5 is 20.

The long run, firms can enter or exit the market, and as a result, the number of firms in each market may change.

In this case, we'll assume that the number of Type A and Type B firms can adjust freely in the long run, and that each firm earns zero economic profit in the long run.

If there are zero economic profits, each firm's total revenue (TR) must equal its total cost (TC), which means that price must equal average total cost (ATC).

For Type A firms, ATC4(q) = TC4(q)/q = 1/q + 2 + q, so:

5 = 1/q + 2 + q

Rearranging and solving for q, we get:

q4 = 2

So each Type A firm will produce 2 units of output in the long run.

For Type B firms, ATCB(q) = TCB(q)/q = 6/q + 2 + 3q, so:

5 = 6/q + 2 + 3q

Rearranging and solving for q, we get:

qB = 1

So each Type B firm will produce 1 unit of output in the long run.

If there are 10 Type A firms and 6 Type B firms, the total quantity produced in the long run when p=5 is:

Qlr = 10q4 + 6qB

= 10(2) + 6(1)

= 26

So, the total quantity produced when p = 5 is 26 in the long run.

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As Almay walks through a local park and passes an old man in pain, the presence of many other walkers in the park will most likely increase the probability that Almay will experience the "bystander effect."

As Almay walks through the local park and comes across an old man who is in pain, the presence of many other walkers in the park will most likely increase the probability that Almay will seek help for the man.

This is because the bystander effect, which is the tendency for individuals to be less likely to intervene in an emergency situation when others are present, is less likely to occur when there are more people around. With more people present, Almay may feel a greater sense of responsibility to act and seek help for the man.

Additionally, the presence of other walkers may also make it easier for Almay to quickly locate someone who can assist with medical attention or call for emergency services.

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#3

Water slides are overrated and roller coasters are dangerous, id rather check out the vr

The exact lengths of the missing sides for the right triangle using trigonometric ratio of the respective angles are: a = 4, b = 4√3, c = 4√3, and d = 4√6

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

sin 30 = a/8 {opposite/hypotenuse}

a = 8 × 1/2 {sin 30 = 1/2}

a = 4

cos 30 = b/8 {adjacent/hypotenuse}

b = 8 × √3/2 {cos 30 = √3/2}

b = 4√3

sin 45 = 4√3/d

d = 4√3 × 2/√2 {sin45 = √2/2}

d = 4√6

cos 45 = c/4√6

c = 4√6 × √2/2

c = 2√12

c = 4√3

Therefore, the exact lengths of the missing sides for the right triangle using trigonometric ratio of the respective angles are: a = 4, b = 4√3, c = 4√3, and d = 4√6

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The domain and the range of the function are given as follows:

The values of x of the function are from an open circle at x = -6 to a closed circle at x = 1, hence the domain is given as follows:

(-6, 1].

The minimum value of the function is y = -2, while the maximum value is an open circle at y = 4, hence the range of the function is given as follows:

[-2, 4).

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Answer:

$200

Step-by-step explanation:

Just divide 1600 by 8

1600 ÷ 8 = 200

Answer:

sara needs to save 200 monthly

Step-by-step explanation:

i just divided 1600 by 8.

hope u have a great day!!

Based on data, it is better to describe the centers of distribution in terms of median because the data distribution is not symmetric. The Option B is correct.

To determine a better measure of center, we must examine the symmetry of the data distribution. We can do it by constructing box plots or dot plots but because we have small data set, we will examine the data visually.

By looking at the data, we see that those distributions are not perfectly symmetric with some values have more spread out than the others. So, it is better to describe the centers of distribution in median rather than in mean.

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