please help me in this question​

Step-by-step explanation:

w = width

2w + 2 =  Length

Area = W x L  = 84 = w (2w+2)

                          84 = 2w^2 + 2w

                            0 = 2w^2 + 2w - 84        Use Quadratic Formula

                                                                 a = 2    b=2    c = -84

to find  

W = 6      then     L =  14 inches

Answer:

Step-by-step explanation:

Answer:  The question is asking us to find the derivative of the function f(x), but the function given is g(x). Therefore, we will assume that the question is asking us to find the derivative of g(x) and proceed accordingly.

To find the derivative of g(x), we need to apply the power rule and the sum rule of derivatives. The power rule states that if f(x) = x^n, then f'(x) = nx^(n-1), and the sum rule states that if f(x) = u(x) + v(x), then f'(x) = u'(x) + v'(x).

Using these rules, we can find the derivative of g(x) as follows:

g(x) = 3x² + 7x - 1

g'(x) = (3x²)' + (7x)' - (1)'

g'(x) = 6x + 7 - 0

g'(x) = 6x + 7

Therefore, the derivative of g(x) is g'(x) = 6x + 7.

Step-by-step explanation:

Answer: We can solve this problem by counting the number of trees that have at least 21 apples and subtracting the number of trees that have at least 80 apples.

Let T be the total number of trees in the orchard, and let n1 be the number of trees that have at least 21 apples, and n2 be the number of trees that have at least 80 apples. Then the number of trees that have at least 21 apples but fewer than 80 apples is:

n1 - n2

To find n1 and n2, we need to know the distribution of the number of apples on each tree. Without this information, we can't find an exact answer. However, we can make some reasonable assumptions and estimate the answer.

Assuming that the number of apples on each tree follows a normal distribution with mean μ and standard deviation σ, we can use the empirical rule (also known as the 68-95-99.7 rule) to estimate the proportion of trees that have at least 21 apples and at least 80 apples. According to this rule:

- Approximately 68% of the trees will have a number of apples within one standard deviation of the mean.

- Approximately 95% of the trees will have a number of apples within two standard deviations of the mean.

- Approximately 99.7% of the trees will have a number of apples within three standard deviations of the mean.

Assuming that the mean number of apples per tree is around 50 (a reasonable estimate based on typical apple orchard data), and that the standard deviation is around 20 (based on empirical data), we can estimate the proportion of trees that have at least 21 apples and at least 80 apples as follows:

The lower bound for the number of apples on a tree that is one standard deviation below the mean is around 30. Therefore, approximately 16% of the trees will have at least 21 apples.

The upper bound for the number of apples on a tree that is two standard deviations above the mean is around 90. Therefore, approximately 2.5% of the trees will have at least 80 apples.

Using these estimates, we can calculate an approximate number of trees that have at least 21 apples but fewer than 80 apples as follows:

n1 - n2 = 0.16T - 0.025T = 0.135T

Therefore, approximately 13.5% of the trees in the orchard have at least 21 apples but fewer than 80 apples. If we know the exact distribution of the number of apples on each tree, we could calculate a more precise answer.

Step-by-step explanation:

Answer:

x=90°

Step-by-step explanation:

As in the angle, there is a box giving us info that x has to be 90°.

But to be sure that there is no mistake we have to do the following:

So we are looking at the surroundings of angle x (which is on a straight line) we see that it is a right angle and look at the angle on the same line is a right angle too.

The equation right angle=90° helps us see that because there are two right angles on a 180° line (90°+90°+180°).

Therefore the answer is:

x=90°

The correct answer is: Both the mean and median are appropriate measures of center.

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves the use of mathematical and computational tools to summarize and analyze large sets of data, with the goal of extracting meaningful insights and identifying patterns or trends.

Here,

The mean is the sum of all salaries divided by the number of salaries. In this case, the sum is:

37,000 + 38,500 + 35,000 + 37,000 + 45,000 + 40,000 + 75,000 = 307,500

And there are seven salaries. Therefore, the mean is:

307,500 / 7 = 43,928.57

The median is the middle value when the salaries are arranged in order from lowest to highest. First, we need to arrange the salaries in order:

35,000, 37,000, 37,000, 38,500, 40,000, 45,000, 75,000

The median is the middle value, which is 40,000.

The mode is the value that appears most frequently in the set of salaries. In this case, both 37,000 and 40,000 appear twice, so there is no unique mode.

Since the salaries are not symmetrically distributed, the mean is not a perfect measure of central tendency. However, it can still provide useful information about the "average" salary. On the other hand, the median is resistant to extreme values and may be a better measure of central tendency for this dataset. Therefore, both the mean and median are appropriate measures of center for this dataset.

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Answer: Using the formula i = prt, we have:

i = (104292.12 - 80040) = 24252.12

p = 80040

t = 3

Substituting these values, we get:

24252.12 = 80040 * r * 3

Solving for r, we get:

r = 0.101 or 10.1%

Therefore, the interest rate is 10.1%.

Step-by-step explanation:

We can show by the uniqueness theorem that the linear transformation, Y = aX + b, is also a normal random variable because the resultant probaility density fnction of Y equals: f(y) = (1/√(2πa^2σX^2)) * exp(-(y-aμX-b)^2/(2a^2σX^2)).

To show that the linear transformation, Y = aX + b is a normal random variable, we need to demonstrate that it satisfies the properties of a normal distribution. This means that it should have a bell-shaped probability density function, mean, and variance.

We can prove that it meets the mean condition this way:

E(Y) = E(aX + b) = aE(X) + b = aμX + b

Next, we can prove that it meets the variance condition thus:

Var(Y) = Var(aX + b) = a^2Var(X) = a^2σX^2

Lastly, the probability density function is given as f(y) = (1/√(2πa^2σX^2)) * exp(-(y-aμX-b)^2/(2a^2σX^2)). This proves that the conditions for a normal random variable is met.

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Answer: The altitude of the triangle is [tex]h = 7 \sqrt{3}.[/tex]

Step-by-step explanation:

Suppose that we separate the equilateral triangle with the altitude of the triangle, as shown in the diagram I attached.

Then the length of the altitude [tex]h[/tex] can be found through the Pythagorean theorem:

[tex]h = \sqrt{14^2-\left( \frac{14}{2} \right)^2} = \sqrt{147} = \boxed{7 \sqrt{3}}.[/tex]

Therefore, the altitude of the equilateral triangle is [tex]h = 7 \sqrt{3}.[/tex]

The statement that (sin 2x) / (1 + cos 2x) = tan x can be proven.

To prove that (sin 2x) / (1 + cos 2x) = tan x, we will use trigonometric identities.

(sin 2x) / (1 + cos 2x)

(2sin x × cos x) / (1 + (cos²x - sin²x))

(2sin x × cos x) / (cos²x + 2sin x × cos x + sin²x)

We can rewrite the denominator using the Pythagorean identity sin²x + cos²x = 1:

(2sin x × cos x) / (1 + 2sin x × cos x)

(2sin x × cos x) × (1 - 2sin x × cos x) / (1 - (2sin x × cos x)²)

((2sin x × cos x) - (4sin²x × cos²x)) / (1 - 4sin²x × cos²x)

(2sin x - 4sin²x) / (1/cos²x - 4sin²x)

Since tan x = sin x / cos x, we can rewrite the expression:

(2tan x - 4tan²x) / (sec²x - 4tan²x)

(2tan x - 4tan²x) / (1 + tan²x - 4tan²x)

(2tan x - 4tan²x) / (1 - 3tan²x)

2tan x × (1 - 2tan²x) / (1 - 3tan²x)

tan x

So, we have proved that (sin 2x) / (1 + cos 2x) = tan x.

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Answer: Spheres aren’t three-dimensional—they are two-dimensional. This is evident from the fact that in order to specify a point on a sphere, you only need two pieces of information, such as latitude and longitude.

If you include the interior of the sphere, this is instead called a closed ball, and that is three-dimensional. You can specify a point in the closed ball in all sorts of different ways; one of the most convenient would be latitude, longitude, and distance from the center. However, other than convenience, there is no reason to prefer one coordinate system over any other.

(This fact has nothing to do with spheres or closed balls—that is just a statement that is generally true. People who insist that “the three dimensions” are length, width, and height don’t know what they are talking about.)

Step-by-step explanation:

The values are;

1. x = 6 ,y = 6√2

2. x = 9√2, y = 18

3. x = y = 9

4. x = 12, y = 12√2

5. x = y = 4√2

6. x = y =( 3√2)/2

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

There are some special angles , in which 45 is part of them.

sin 45 = 1/√2

cos 45 = 1/√2

tan 45 = 1

1. x = 6 ( isosceles triangle)

y = 6 × √2 = 6√2

2. x = 9√2 ( isosceles triangle)

y = 9√2 × √2 = 9×2 = 18

3. x = 9√2/√2 = 9

x = y = 9 ( isosceles triangle)

4. x = 12 ( isosceles triangle)

y = 12×√2 = 12√2

5. x = 8/√2 = 8√2/2 = 4√2

x = y = 4√2( isosceles triangle)

6. x = 3/√2 = (3√2)/2

x = y =( 3√2)/2 ( isosceles triangle)

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To solve the equation x^2 + 4x - 11 = 0 by completing the square, we can follow these steps:

Move the constant term to the right side of the equation:

x^2 + 4x = 11

Complete the square by adding the square of half the coefficient of x to both sides of the equation:

x^2 + 4x + (4/2)^2 = 11 + (4/2)^2

Simplifying the left side:

x^2 + 4x + 4 = 11 + 4

Factor the perfect square on the left side of the equation:

(x + 2)^2 = 15

Take the square root of both sides of the equation:

x + 2 = ±√15

Solve for x by subtracting 2 from both sides:

x = -2 ± √15

Therefore, the solutions to the equation x^2 + 4x - 11 = 0 by completing the square are x = -2 + √15 and x = -2 - √15.

Answer:

[tex]3f(2) = 3( {2}^{2} ) = 3(4) = 12[/tex]

Answer: x = -1 and x = 9

Step-by-step explanation:

Lets solve this equation step by step

1. Simplify both sides of the equation

x^2 - 8x + 16 = 25

2. Subtract 25 from both sides

x^2 - 8x + 16 - 25 = 25 - 25

3. Factor the left side of the equation

(x + 1) (x - 9) = 0

4. Set the factors equal to zero

x + 1 = 0 or x - 9 = 0

Thus your answers are x = -1 and x = 9

You can check by inputting the values into the original equation

(-1 - 4)^2 = 25 and (9 - 4)^2 = 25

Answer:

39.96

Step-by-step explanation:

the shape is a parallelogram ao the formula is base x height

A=10.8 x 3.7

A=39.97

1. In the Robinson version, Truth asks "And ain't I a woman?" four times, while in the Gage version she only asks it three times. 2. It is important to hear both versions of the speech because they highlight the ways in which historical documents can be altered and manipulated over time. 3. The differences between the two versions of the speech likely changed the way people in the north and south understood the context of her speech in significant ways. 4. Hearing the differences in dialect changes the way we think about the speech by highlighting the unique voice and perspective of the speaker.

Speech is the act of expressing thoughts, ideas, or emotions through spoken words. It is a form of communication that allows individuals to convey information, share opinions, ask questions, and express feelings to others.

1. Three differences between the Robinson version and the Gage version of the speech are:

In the Robinson version, Truth says "I have as much muscle as any man" while in the Gage version she says "I have ploughed and planted, and gathered into barns, and no man could head me!".

In the Robinson version, Truth asks "And ain't I a woman?" four times, while in the Gage version she only asks it three times.

In the Robinson version, Truth refers to herself as a "colored woman" while in the Gage version she uses the term "African American".

2. It is important to hear both versions of the speech because they highlight the ways in which historical documents can be altered and manipulated over time. The differences between the two versions show how editors and publishers can change the meaning and impact of a text by making small modifications to it. Additionally, hearing both versions allows us to appreciate the nuances of language and dialect, and how different speakers can bring their own interpretations and emphasis to a text.

3. The differences between the two versions of the speech likely changed the way people in the north and south understood the context of her speech in significant ways. For example, the reference to "colored women" in the Robinson version would have been seen as more confrontational and controversial in certain regions. Today, the differences may help us appreciate the diversity and complexity of language, and how it reflects the cultural and historical contexts in which it is spoken.

4. Hearing the differences in dialect changes the way we think about the speech by highlighting the unique voice and perspective of the speaker. The dialect used in each version reflects the cultural and historical context of the time, and the different audiences that the speeches were intended for. By hearing the dialect of each version, we can better appreciate the ways in which language shapes our understanding of history and identity.

As for the next set of questions:

When women's rights activists spoke out, they were advocating for both white women and African-American women, although the experiences and struggles of African-American women were often ignored or marginalized within the movement.

Truth makes several distinct arguments in her speech, including that women deserve the same rights and respect as men, that the stereotype of women as weak and dependent is unjust, and that the experiences of African-American women are often overlooked in discussions of women's rights.

Truth is saying that women deserve equal rights and respect as men, and that the societal norms that limit women's opportunities and autonomy are unjust and unfounded.

Truth is arguing that women need to fight for their own rights, rather than waiting for men to give them these rights. She also emphasizes the importance of solidarity and mutual support among women.

Truth's speech reflects intersectionality by recognizing the ways in which race and gender intersect to create unique experiences of oppression and marginalization. She argues that the struggles of African-American women cannot be separated from the struggles of all women, and that a truly equitable society must address the needs and concerns of all marginalized groups. One passage that reflects this is when she says, "I have borne thirteen children, and seen most all sold off to slavery, and when I cried out with my mother's grief, none but Jesus heard me! And ain't I a woman?" This passage highlights the intersection of race, gender, and motherhood in Truth's experience.

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We find that P(Z > 2.46) is roughly 0.007 using a calculator or a basic normal distribution table. The probability that a bag will contain more than 20% blue jellybeans is therefore approximately 0.007 or 0.7%.

The probability of an event is the ratio of good outcomes to all other potential outcomes. The number of successful outcomes for an experiment with 'n' outcomes can be expressed using the symbol x.

Here in the question,

We can utilise the binomial distribution formula to resolve this issue. In a bag of 200 jelly beans, let X represent the proportion of blue jelly beans. Following that, X exhibits a binomial distribution with parameters of n = 200 and p = 0.15, where p is the likelihood of drawing a blue jellybean.

The formula for determining the likelihood of finding more than 20% blue jellybeans in a bag is:

P (X > 0.2 × 200) = P (X > 40)

Since n is large (200) and p is not too near to 0 or 1, we can utilise the usual approximation to the binomial distribution. We may determine the equivalent mean and standard deviation of the normal distribution by using the mean and variance of the binomial distribution:

μ = np = 200 × 0.15 = 30

σ = √ (np(1-p)) = √ (200 × 0.15 × (1-0.15)) = 4.07

Then, we can standardize the random variable X as:

Z = (X - μ) / σ

So, we have:

P(X > 40) = P((X - μ) / σ > (40 - μ) / σ)

= P(Z > (40 - 30) / 4.07)

= P(Z > 2.46)

We find that P(Z > 2.46) is roughly 0.007 using a calculator or a basic normal distribution table. The likelihood that a bag will contain more than 20% blue jellybeans is therefore approximately 0.007 or 0.7%.

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Sample space = { {C; H; W}; {C; H; F}; {C; B; W}; {C; B; F}; {C; S; W}; {C; S; F}.... }

Continue listing by replacing C with M & V, e.g {M; H; W}; {M: H; F}; {M; B; W}

Answer:

C) 4

Step-by-step explanation:

Answer:

the answer is 110-23i

The probability that a person phones the cable company and waits between 10 to 20 minutes for service is approximately 0.0729, or about 7.29%.

What is the mean and standard deviation?

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

We can start by standardizing the values using the z-score formula:

z = (x - μ) / σ

where:

x = the wait time in minutes

μ = the population mean (average wait time of 28 minutes)

σ = the population standard deviation (5.5 minutes)

For x = 10 minutes:

z = (10 - 28) / 5.5 = -3.27

For x = 20 minutes:

z = (20 - 28) / 5.5 = -1.45

Next, we can use a standard normal distribution table (or a calculator or software) to find the area under the standard normal curve between these two z-scores.

Using a standard normal distribution table, we can find that the area to the left of z = -1.45 is 0.0735, and the area to the left of z = -3.27 is 0.0006. Therefore, the area between z = -3.27 and z = -1.45 is:

0.0735 - 0.0006 = 0.0729

Hence, the probability that a person phones the cable company and waits between 10 to 20 minutes for service is approximately 0.0729, or about 7.29%.

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The length of side AB is given as follows:

[tex]AB = \frac{6}{\sqrt{3}}[/tex]

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For the angle of 30º, we have that:

Hence the length of side AB is obtained as follows:

tan(30º) = AB/6

AB = 6 x tan(30º)

[tex]AB = 6 \times \frac{1}{\sqrt{3}}[/tex]

[tex]AB = \frac{6}{\sqrt{3}}[/tex]

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The value of the side AB is calculated as: AB = 6/√3

There are different trigonometric ratios used in right angle triangles which are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

Looking at the given triangle, the value of AB can be gotten via the trigonometric ratio tan x. Thus:

AB = 6 * tan 30

AB = 6 * 1/√3

AB = 6/√3

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Statistics is a branch of mathematics that involves the collection, analysis, interpretation, presentation, and organization of data. It is used in a wide range of fields such as science, engineering, social sciences, business, economics, and more.

In statistics, data is collected through various methods such as surveys, experiments, and observations. This data is then analyzed using statistical methods to extract meaningful insights, identify patterns and relationships, and make informed decisions.

Some common statistical techniques include descriptive statistics, inferential statistics, hypothesis testing, regression analysis, and probability theory. These techniques are used to help researchers and analysts to understand and draw conclusions about data, and to test whether their conclusions are statistically significant.

Statistics has many practical applications, such as market research, medical research, quality control, risk assessment, and many others. It plays a critical role in modern society, helping individuals and organizations make informed decisions based on data-driven insights.

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The truth table is given above for (A ⋀ B) → C.

What is the logical statement?

A logical statement, also known as a proposition or a statement of fact, is a declarative sentence that is either true or false, but not both. It is a statement that can be evaluated based on the available information or evidence to determine its truth value. In other words, a logical statement is a statement that can be either true or false, but not both.

To create a truth table for the logical statement (A ⋀ B) → C, we need to consider all possible combinations of truth values for propositions A, B, and C.

There are 2 possible truth values (true or false) for each proposition, so there are 2³ = 8 possible combinations.

We can organize these combinations into a table as follows:

| A | B | C | (A ⋀ B) | (A ⋀ B) → C |

|---|---|---|---------|-------------|

| T | T | T |    T    |      T      |

| T | T | F |    T    |      F      |

| T | F | T |    F    |      T      |

| T | F | F |    F    |      T      |

| F | T | T |    F    |      T      |

| F | T | F |    F    |      T      |

| F | F | T |    F    |      T      |

| F | F | F |    F    |      T      |

In this table, the column labeled (A ⋀ B) represents the truth value of the conjunction of A and B (i.e., A AND B), and the column labeled (A ⋀ B) → C represents the truth value of the conditional statement (A ⋀ B) → C.

The symbol "T" represents "true" and the symbol "F" represents "false".

Hence, The truth table is given above for (A ⋀ B) → C.

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The statistical question that can result in numerical data is "How many hours this week did you spend on homework?"

The statistical question that can result in numerical data is "How many hours this week did you spend on homework?"

This is because the question is asking for a numerical response that can be measured and counted. The other options are not statistical questions that can result in numerical data.

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Answer:

Step-by-step explanation:

2.1 so a

The diameter of the semicircle is with an area of 76.97 square yards is 14 yards.

Semicircle is half that of a circle, hence the area will be half that of a circle. Area of semi circle = 1/2 × πr²

Where r radius and π is constant pi.

Since we are given the area of the semicircle as 76.97 square yards, we can set up the following equation:

76.97 = 1/2 × (πr²)

Multiplying both sides by 2, we get:

153.94 = πr²

Dividing both sides by π, we get:

r² = 49

Taking the square root of both sides, we get:

r = 7

Therefore, the diameter of the semicircle is: d = 2r  = 2(7) = 14 yards

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Answer:

(x - 5)² + (y + 6)² = 16

Step-by-step explanation:

assuming you require the equation of the circle

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (5, - 6 ) and r = 4 , then

(x - 5)² + (y - (- 6) )² = 4² , that is

(x - 5)² + (y + 6)² = 16

Step-by-step explanation:

a) factorize A

A = (2x-1)²+2(3-6x)(4x-7)-4x²+1

expand the terms

(2x-1)²-52x²+108x-41

factorize

(2x-1)²-(26x-41)(2x-1)

factor out the common factor 2x-1

-(2x-1)(24x-40)

A = -8(2x-1)(3x-5)

b) show that B = (3x-11)(2x-1)

6x²-25x+11

6x²-3x-22x+11

3x(2x-1)-11(2x-1)

(2x-1)(3x-11)

c) Expand and reduce A

(2x-1)²+2(3-6x)(4x-7)-4x²+1

-48x²+108x-40

d) Calculate A for x=0 and x=-1

when x=0 -48(0)²+108(0)-40

A=0

x=-1 -48(-1)²+108(-1)-40

A=-196

e) Reduce 2A-3B

A=-48x²+108x-40 B=6x²-25x+11

2(-48x²+108x-40)-3(6x²-25x+11)

-96x²+216x-80-18x²+75x-33

-144x²+291x-113

f) Factorize 2A-B

A=-48x²+108x-40 B=6x²-25x+11

2(-48x²+108x-40)-(6x²-25x+11)

-96x²+216x-80-6x²+25x-11

-102x²+241x-91

x=(241 + sqrt(20953))/204

x=(241 - sqrt(20953))/204

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