Help with the following 2 problems please

The length of AB of the parallelogram is determined as 14.36 inches.

The length of AB of the parallelogram can be determined by applying cosine rule as shown below:

The cosine rule, also known as the law of cosines, is a mathematical formula that relates the lengths of the sides of a triangle to the cosine of one of its angles. It is commonly used to find the length of an unknown side or the measure of an unknown angle in a triangle when the lengths of two sides and the measure of the included angle are known.

Length AB = Length AD = x

DB² = AB² + AD² - 2(AB x AD) cos (A)

22² = x² + x² - 2x²(cos 100)

484 = 2x² + 0.347x²

484 = 2.347x²

x² = 484/2.347

x² = 206.2

x = √206.2

x = 14.36 inches

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The vector v+w has a magnitude of 2√2 and its direction is along the positive x-axis.

What is meant by vector?

A vector is a quantity that has both magnitude and direction. It is represented as an arrow with its length representing the magnitude and its direction representing the direction of the quantity.

What is meant by the x-axis?

The x-axis is the horizontal line on a coordinate plane that is used as a reference for plotting and describing the positions of points in two-dimensional space. It is often referred to as the "horizontal axis" or the "abscissa".

According to the given information

Here the vector v has a magnitude of 2 and a direction of 45° so the components of vector v are:

v_x = 2 cos 45° = √2

v_y = 2 sin 45° = √2

Vector w has a magnitude of 2 and a direction of 45° South of East. This means that the angle between vector w and the positive x-axis is 45°, and the angle between vector w and the negative y-axis is 45°. Therefore, the components of vector w are:

w_x = 2 cos 45° = √2

w_y = -2 sin 45° = -√2

Now we can add the components of vectors v and w to find the components of the vector v+w:

(v+w)_x = v_x + w_x = √2 + √2 = 2√2

(v+w)_y = v_y + w_y = √2 - √2 = 0

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Domain and range of function is (D)=D={x|x≥2}, R={y|y≥0}.

In mathematics, the domain of a function is the set of all possible input values for which the function is defined. The range of a function is the set of all possible output values that the function can produce, based on its input values. In other words, the domain is the set of all x-values that the function can take, while the range is the set of all corresponding y-values that the function can take.

The given graph is oriented toward x direction

Domain of function =x≥2

For every value of x the y is always positive

So, range =y≥0

Hence, domain and range of function is (D)=D={x|x≥2}, R={y|y≥0}

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Matching each function with the transformation that took place gives:

g(x) = -(x - h)ⁿ: Reflection across the x-axis

j(x) = axⁿ + k: Translation of k units up

m(x) = (x + h)ⁿ - k: Translation of h units to the left

Vertical dilation: Functions of form f(x) = 2ⁿ are vertically dilated.

In mathematics, a transformation refers to a process of changing the size, position, or orientation of a geometric object or a function.

Transformations are usually expressed as a set of rules or equations that determine how each point or element in the original object or function maps to a corresponding point or element in the transformed object or function. Common types of transformations include translations, rotations, reflections, dilations, and combinations of these operations.

Transformations are widely used in many areas of mathematics, physics, engineering, and computer science to study and model complex systems and phenomena.

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The height of the parallelogram is equal to the diameter of the circle. The base of the parallelogram is equal to half of the circumference of the circle. Therefore, the area of the circle (πr2) is equal to bh and the circumference of the circle is equal to 2b.

The height of the parallelogram is equal to the diameter of the circle. This can be seen because each of the eight sectors has the same area, so they are all the same size. If we place them next to each other in the shape of a parallelogram, we can see that the height of the parallelogram is equal to the diameter of the circle.

The base of the parallelogram is equal to half of the circumference of the circle. This is because the circumference of the circle is divided equally into eight sectors, and the base of the parallelogram is formed by placing two adjacent sectors together. Therefore, the base of the parallelogram is equal to the arc length of one sector plus the arc length of its adjacent sector. Each sector is 1/8th of the circle, so the arc length of one sector is 1/8th of the circumference. Adding the arc lengths of two adjacent sectors gives 1/4th of the circumference, which is half of the base of the parallelogram.

Therefore, the area of the circle (πr2) is equal to the area of the parallelogram (bh), where h is the diameter of the circle and b is half of the circumference of the circle. Additionally, the circumference of the circle is equal to the base of the parallelogram multiplied by 2.

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The probability that 3 boys are selected for the relay team given that the first election was a girl is approximately 0.122, or 12.2%.

Let B represent the decision to select three boys for the relay team whereas A represents the scenario when a girl was chosen first.

P(B|A) is the conditional probability of B given A.

The Bayes theorem gives us:

P(B|A) is equal to P(A|B)*P(B)/P(A).

Given that the relay team consists of 3 boys, the probability that a girl would be chosen as the first team member is P(A|B). Therefore:

P(A|B) = 7/13 * 6/12 * 5/11 * 7/10 = 0.0871

P(B) represents the likelihood of choosing three males for the relay team in an arbitrary manner.

P(B) = (7C3 * 7C1) / (14C4) = 35/143

P(A) represents the likelihood that a girl will be chosen as the first team member without any restrictions.

P(A) = 7/14 = 1/2

Combining everything, we get the following: P(B|A) = P(A|B) * P(B) / P(A) = 0.0871 * 35/143 / (1/2) = 0.1220.122, or 12.2%.

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The changes that Jason should make are:

1. Plan a trip not during the tourist season.

2. In place of renting car, use transportation services of the country.

3. He should go to other places to find a nice hotel.

The solution has been obtained by using cost planning.

What is cost planning?

Estimating expenses, establishing an agreed-upon budget, and managing actual and projected expenditures in relation to that budget are all parts of cost planning and control.

The changes that Jason should make are:

1. Plan a trip not during the tourist season. This is because during the tourist season prices are high.

2. In place of renting car, use transportation services of the country. This is because the local transport will cost him less that the rental.

3. He should go to other places to find a nice hotel. This is because central Turkey is costly and he might find a nice hotel in other areas in less price.

Hence, the required solution has been obtained.

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If 31.2 out of every 100 pregnant women in India deliver their babies by C-section.

First, we need to find the fraction of pregnant women who deliver by C-section

31.2 out of 100 = 31.2/100 = 0.312

Then, we can use this fraction to find the number of pregnant women out of 85,733 who would be expected to deliver by C-section.

0.312 x 85,733 = 26,723.896

Rounding to the nearest whole number, we get

26,724 pregnant women.

26,724 pregnant women out of 85,733 would be expected to deliver by C-section.

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Answer:

x = 35

Step-by-step explanation:

since the figures are similar then the ratios of corresponding parts are in proportion, that is

[tex]\frac{x}{10}[/tex] = [tex]\frac{14}{4}[/tex] = [tex]\frac{7}{2}[/tex] ( cross- multiply )

2x = 7 × 10 = 70 ( divide both sides by 2 )

x = 35

If Joan has a square flower bed with a side length of 4 meters filled with tulips, the density of tulips in the bed is 22.1 tulips per square meter.

To find the density of tulips for the area of the bed, we need to divide the total number of tulips by the area of the bed. The area of the square flower bed is the side length squared, so in this case, it is 4 meters x 4 meters = 16 square meters.

So, the density of tulips in the bed is 354/16 ≈ 22.1 tulips per square meter. This means that there are approximately 22.1 tulips growing in every square meter of the flower bed.

The density is a measure of the amount of something per unit of space, so in this case, it is the number of tulips per square meter. It is a useful metric for understanding how many of something is present in a given area, which can be important for planning and management purposes.

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1. The equation for the function is defined as follows: g(x) = (1/3)^x - 2.

2. The range of the function is given as follows: The set of real numbers less than -5.

An exponential function has the definition presented as follows:

y = ab^x.

In which the parameters are given as follows:

For item 1, the function has an horizontal asymptote at y = -2, hence it is defined as follows:

y = a(1/3)^x - 2.

When x = 0, y = -1, hence the parameter a is obtained as follows:

-1 = a - 2

a = 1.

Thus the function is:

g(x) = (1/3)^x - 2.

For item 2, we have that the function is:

Hence the range of the function is given as follows:

The set of real numbers less than -5.

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Based on the information provided, the polygon can be classified as a trapezoid.

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The meaning of V(2) is the Erica's vertical distance after walking 2 kilometers along the trail.

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The input and output variables for this problem are given as follows:

V(2) means that the number of km is of 2, hence the meaning of V(2) is the Erica's vertical distance after walking 2 kilometers along the trail.

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Here is an example of how to create an object model, UML diagrams, and contract obligations in general.

Let's have a look at a basic "Bank Account" system, where a customer may deposit money, withdraw it, and see the amount of their account. The following classes would be represented in the UML class diagram for this system:

Bank Account Client

The following characteristics would be included in the Bank Account class:

string Account Number

stability: float

and the subsequent techniques:

deposit(float amount) = None

withdrawal(float :amount) = None

float: check Balance()

The following characteristics would apply to the Customer class:

string name

list of accounts[Bank Account]

and the subsequent techniques:

account: Bank Account; add account(account) -> None

account: Bank Account; remove  Account(account: None)

Bank Account: get  Account(Account number: string)

For the Bank Account class, the design by contract obligations would be:

Pre-conditions:

amount > 0

withdraw(amount): amount > 0 and balance >= amount

Check Balance(): None

Post-conditions:

deposit(amount): balance += amount

withdraw(amount): balance -= amount

Check Balance(): return balance

The design by contract responsibilities for the Customer class would be:

Pre-conditions:

Add account(account): account not in accounts

Post-conditions:

Add account(account): accounts. append(account)

remove (account): accounts.

get account (account number): return the Bank Account object with the given account Number.

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The quantity of pounds of dog food that Mrs. Evans should buy that would be enough for her dog = 720 ounces.

The total number of days the food is required to last = 90 days.

The quantity of dog food in ounce the dog eat per day = 4 × 2 = 8 ounces.

Therefore the quantity of pounds that will be enough for the dog for the whole 90 days would be = ?

That is;

1 day = 8 ounces

90 days = X

Make X the subject of formula;

X = 90× 8

= 720 ounces

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On day zero, the number of students who know the rumor are 2 people who are Susanna and Liz.

On day 2, the number of students would be 12 students.

The number of days till 32 students know the rumor is 6 days.

2 students (Susanna and Liz) know the rumor on day 0.

On day 2, the number of students who know the rumor will be the initial number of students (2) plus 5 students for each day that has passed (5 * 2 = 10). So, on day 2, 2 + 10 = 12 students know the rumor.

To find the number of days it will take for 32 students to know the rumor, we can set up an equation using the given information:

2 (Susanna and Liz) + 5 x number of days = 32

Now, we can solve for the number of days:

5 x number of days = 32 - 2

5 x number of days = 30

number of days = 30 / 5

number of days = 6

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Step-by-step explanation:  

1. Quota Sampling: This method involves identifying specific subgroups of respondents that need to be included in the study in a specific proportion to the population.

2. Convenience Sampling: This sampling technique involves selecting the sample based on the availability of participants at the time of the study.

3. Stratified Sampling: This technique divides the population into subgroups or strata based on similarities, with the elements within each group being relatively homogeneous and heterogeneous among the other subgroups.

4. Purposive Sampling: This type of sampling is based on the intention or purpose of the study, and the sample is selected based on the researcher's judgment or knowledge of the population.

5. Judgment Sampling: This sampling technique depends on some pre-set standards, and the representative sample is selected based on the researcher's judgment or experience. 6. Simple Random Sampling: This technique involves using randomization to ensure that every element of the population has an equal chance of being selected for the sample. 7. Snowball Sampling: This sampling method is used in situations where the population is completely unknown or rare, and it relies on referrals from the initial participants to identify subsequent participants.

8. Hypothesis Sampling: This type of sampling is guided specifically by a hypothesis, and the sample is selected based on the research question being asked.

9. Qualitative Sampling: This technique is used in qualitative research and involves a systematic, subjective approach used to describe life experiences and give them meaning.

LO. Quantitative Sampling: This technique involves an objective, systematic, empirical investigation of observable phenomena through the use of computational techniques.

The height of the rectangular prism is 8 inches.

A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles.

The volume of a rectangular prism is expressed as;

V = w × h × l

Where w is the width, h is height and l is length

Given that:

Volume V = 241.92 in³

Length l = 5.6 in

Width w = 5.4 in

Height h = ?

Plug the given values into the above formula and solve for h

V = w × h × l

h = V / ( w × l )

h = 241.92 in³ / ( 5.4 in × 5.6 in )

h = 8 in

Therefore, the height is 8 inches.

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Answer:

  7²

Step-by-step explanation:

You want to know what 7×7 is when it is written using an exponent.

At its most basic, an exponent signifies repeated multiplication. It represents the number of times a value appears as a factor in the product.

The expression 7×7 has 7 as a factor 2 times. It can be written as 7 with an exponent of 2.

  7×7 = 7²

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The length of the other side will be 3.

To obtain the length of the other side of the rectangle, given the approximation of 1.62, we will first divide 4.9, the known side by x, the unknown side, and equate this to 1.62.

If we are using the approximation of 1.62, then the length of the other side of the rectangle will be 4.9/x = 1.62

1.62x = 4.9

x = 3

So, the length of the other side, which in this case is shorter is 3.

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The equation to calculate the cost of her shoes without shipping included is: x = 55.25

Let x be the cost of Carly's shoes.

The problem states that the total cost of her purchase (including shoes and shipping) is $60.75, so we can set up the equation:

x + 5.50 = 60.75

To find the cost of her shoes without shipping, we need to isolate x. We can do this by subtracting 5.50 from both sides:

x + 5.50 - 5.50 = 60.75 - 5.50

Simplifying:

x = 55.25

Therefore, the equation to calculate the cost of her shoes without shipping included is: x = 55.25

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Answer:

266

Step-by-step explanation:

36 hours x 7 people.

Hope this helps...

Please mark me brainliest.

Answer: 266 hours

Step-by-step explanation:

38 x 7 = 266 hours. Each worker worked 38 hours, and there are 7 people. So, multiply worker by time.

The 90% confidence interval estimate of the population mean calories in a lunch box after the change is between 524.2 and 531.8.

(a) The point estimate of the population proportion of lunch boxes provided by "Better Lunch" had calories above 650 is 0.09, which is equal to 27/300.

(b) The sampling error at 98% confidence level for the estimate of the population proportion can be calculated using the following formula:

Sampling error = z*(standard deviation/square root of sample size)

Where z is the critical value at 98% confidence level, which can be found using a standard normal distribution table or calculator. For a 98% confidence level, the z value is 2.33.

Substituting the values, we get:

Sampling error = 2.33*(sqrt(0.09*0.91/300)) = 0.049 or 4.9%

Therefore, the sampling error at 98% confidence level for the estimate of the population proportion of lunch boxes provided by "Better Lunch" had calories above 650 is 4.9%.

(c) The 98% confidence interval estimate of the population proportion of lunch boxes provided by "Better Lunch" had calories above 650 can be calculated using the following formula:

Confidence interval = point estimate ± (z*standard error)

Where point estimate is 0.09, z is the critical value at 98% confidence level which is 2.33, and standard error is the standard deviation divided by the square root of sample size.

Substituting the values, we get:

Confidence interval = 0.09 ± (2.33*sqrt(0.09*0.91/300)) = 0.09 ± 0.114 or (0.026, 0.154)

Therefore, the 98% confidence interval estimate of the population proportion of lunch boxes provided by "Better Lunch" had calories above 650 is between 0.026 and 0.154.

(d) After the menu update, the sample mean of the calories of the above sample can be calculated as follows:

New sample mean = 0.96 * 550 = 528

The sample standard deviation after the change is still 40, assuming the variability of calories is not affected by the menu update.

To construct a 90% confidence interval estimate of the population mean calories in a lunch box after the change, we can use the following formula:

Confidence interval = sample mean ± (t*standard error)

Where t is the critical value at 90% confidence level with degrees of freedom (df) = sample size - 1. Using a t-distribution table or calculator with df = 299, we find that t = 1.645.

The standard error can be calculated as follows:

Standard error = standard deviation/sqrt(sample size) = 40/sqrt(300) = 2.31

Substituting the values, we get:

Confidence interval = 528 ± (1.645*2.31) = 528 ± 3.8 or (524.2, 531.8)

Therefore, the 90% confidence interval estimate of the population mean calories in a lunch box after the change is between 524.2 and 531.8.

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G. y = 37/24x

Direct variation means that the number of inches of rain (y) is directly proportional to the number of hours (x). In this case, 37 inches of rain fell in a 24-hour period. To find the constant of proportionality, divide the total inches of rain by the total hours:

k = 37 inches / 24 hours

Now, we can write the equation of direct variation:

y = kx

Substitute the value of k:

y = (37/24)x

The equation of the line that passes through the points (4, 1) and (12, -3) is y = (-1/2)x + 3.

Explain the term equation

An equation is a mathematical statement that expresses the equality of two expressions or values. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used to represent relationships between quantities and to solve problems in various fields, including mathematics, physics, and engineering.

According to the given information

We can use the point-slope form of the equation of a line to find the equation of the line that passes through the two given points.

The point-slope form of the equation of a line is:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is a point on the line.

To find the slope of the line that passes through (4, 1) and (12, -3), we can use the slope formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) = (4, 1) and (x2, y2) = (12, -3)

m = (-3 - 1) / (12 - 4) = -4 / 8 = -1/2

Now that we have the slope of the line, we can use one of the two given points and the slope to find the equation of the line. Let's use the point (4, 1):

y - y1 = m(x - x1)

y - 1 = (-1/2)(x - 4)

Distributing the -1/2, we get:

y - 1 = (-1/2)x + 2

Adding 1 to both sides, we get:

y = (-1/2)x + 3

Therefore, the equation of the line that passes through the points (4, 1) and (12, -3) is y = (-1/2)x + 3.

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Answer:

16.58. my answer needs to be more than 20 characters, soooo... how is your day going?

The length of LG in the plane is

To find the distance between two points in a 2D plane, we can use the distance formula:

distance = √((x2 - x1)^2 + (y2 - y1)^2)

Using this formula, we can find the distance between L(4,4) and G(9,9):

distance = √((9 - 4)^2 + (9 - 4)^2)

= √(5^2 + 5^2)

= √50

= 5√2

Therefore, the distance between L(4,4) and G(9,9) is 5√2, which is approximately 7.07 units.

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