What is the area of the triangle?

90 square yards
45 square yards
120 square yards
60 square yards

Answer:

I think its an obtuse angle. Not sure what answers would be though

Answer:

∠AFE=140°

Step-by-step explanation:

First you have to find x angle because it will correspond with the DFE angle and then you can find the AFE angle.

To do this, you add angles BFC and CFD. BFC is 50° and CFD is 90° (because it is a right angle). 50+90=140°. Then to find x, you subtract 140° from 180°, which is 40°. So x=40°.

Then, since you know that x corresponds with angle DFE, you subtract 40°(x/DFE angle) from 180°(straight line) and you get 140°. So, ∠AFE=140°.

:) ur welcome

The consecutive integers such 4 that times the smaller integer is 50 less than 6 times the larger integer are 22 and 23.

Let the consecutive integers be x and x + 1.

In this case, the integers are such 4 that times the smaller integer is 50 less than 6 times the larger integer.

This will be:

4(x) = 6(x + 1) - 50

4x = 6x + 6 - 50

Collect like terms

4x - 6x = -44

-2x = -44

Divide

x = 44/2

x = 22

Also, x + 1 = 22 + 1 = 23

The numbers are 22 and 23.

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Here's the LaTeX representation of the given explanation:

To find the equation of the tangent plane to the surface at the point \(\((1, 3, -4)\)\) , we need to find the partial derivatives of the given surface equation with respect to \(\(x\)\) and \(\(y\).\)

Given surface equation: \(\(z = 8x^2 y^2 - 7y\)\)

Partial derivative with respect to \(\(x\)\) :

\(\(\frac{{\partial z}}{{\partial x}} = 16xy^2\)\)

Partial derivative with respect to \(\(y\)\) :

\(\(\frac{{\partial z}}{{\partial y}} = 16x^2y - 7\)\)

Now, we can use these partial derivatives to find the equation of the tangent plane. The equation of a plane can be written as:

\(\(z - z_0 = \frac{{\partial z}}{{\partial x}}(x - x_0) + \frac{{\partial z}}{{\partial y}}(y - y_0)\)\)

where \(\((x_0, y_0, z_0)\)\) is the point on the surface \(\((1, 3, -4)\)\) at which we want to find the tangent plane.

Substituting the values, we have:

\(\(z - (-4) = (16xy^2)(x - 1) + (16x^2y - 7)(y - 3)\)\)

Simplifying this equation, we get:

\(\(z + 4 = 16xy^2(x - 1) + 16x^2y(y - 3) - 7(y - 3)\)\)

Expanding and collecting like terms, we have:

\(\(z + 4 = 16x^2y^2 - 16xy^2 + 16x^2y - 48x^2y - 7y + 21\)\)

Combining like terms, we get:

\(\(z + 4 = 16x^2y^2 - 16xy^2 - 32x^2y - 7y + 21\)\)

Finally, rearranging the equation to the standard form of a plane, we have:

\(\(16x^2y^2 - 16xy^2 - 32x^2y - 7y + z - 25 = 0\)\)

So, the equation of the tangent plane to the given surface at the point \(\((1, 3, -4)\)\) is \(\(16x^2y^2 - 16xy^2 - 32x^2y - 7y + z - 25 = 0\).\)

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The average rate of change of f(x), represented by the table is 13

The formula for calculating the rate of change which is also known as the slope is expressed as;

Rate of change = f(b)-f(a)/b-a

Using the interval [1 3]

f(1) = 3^1 = 1

f(3) = 3^3 = 27

Substitute

Rate of change = 27-1/3-1

Rate of change= 26/2

Rate of change= 13

Hence the average rate of change of f(x), represented by the table is 13

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It looks like we have

\(f(x)=\begin{cases}5-x&\text{for }x<5\\8&\text{for }x=5\\x+3&\text{for }x>5\end{cases}\)

and we want to find \(\lim\limits_{x\to5}f(x)\).

Since \(x\) is approaching 5, we don't care about the value of \(f(x)\) when \(x=5\).

We do care about how \(f(x)\) behaves to either side of \(x=5\). If \(x\to5\) from below, then \(f(x)=5-x\), so that

\(\displaystyle\lim_{x\to5^-}f(x)=\lim_{x\to5}(5-x)=5-5=0\)

On the other hand, if \(x\to5\) from above, then \(f(x)=x+3\), so that

\(\displaystyle\lim_{x\to5^+}f(x)=\lim_{x\to5}(x+3)=5+3=8\)

The one-sided limits do not match, since 0 ≠ 8, so the limit does not exist.

The dimensions of the garden are 12.5 feet by 30.5 feet.

To model this situation, we can use two equations. Let the width of the rectangular garden be w feet and the length be l feet.

Then:We know that the perimeter of the garden is 90 feet because the amount of fencing used was 90 feet.Perimeter = sum of all sides2(l + w) = 90Divide both sides by 22(l + w)/2 = 45l + w = 45Now,

we also know that the length of the fence, 1, was 5 feet less than 3 times the width,

w.l = 3w - 5Substitute this equation for l in the first equation:3w - 5 + w = 45Simplify:4w - 5 = 45

Add 5 to both sides :4w = 50Divide both sides by 4:w = 12.5

Now that we know the width of the garden is 12.5 feet, we can use the equation for l to find the length:l = 3w - 5l = 3(12.5) - 5l = 30.5

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a). The R² of 0.9128 indicates that the model explains 91.28% of the variation in unemployment rates.

b) To find the average unemployment rate in the early fourth quarter period of 1966 with constant vacancy levels, set D = 0 in the regression equation: UN = 2.7491 - 1.5294V.

a. The regression results show that the unemployment rate (UN) is influenced by job vacancies (V), the time period (D), and their interaction (D.V.). T

he positive coefficient for D (1.1507) indicates a higher unemployment rate after 1966-IV due to policy changes, while the negative coefficients for V (-1.5294) and the interaction term (-0.8511) imply that a higher job vacancy rate reduces unemployment, with this effect being less pronounced after 1966-IV.

b. Then, plug in the vacancy rate (V) to calculate the average unemployment rate.

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The total number of candies in the store is 312. It is obtained by using the concept of exponent and power on the given problem.

What is an Exponent?

The number of times a quantity is multiplied by itself is referred to as an exponent or power of the given quantity. For eg: 25, where 5 is an exponent or power of 2 and 2 is called the base of exponent 5. Any quantity raised to the power 0 always returns 1 as result.

Calculation of the total number of candies in the store

(36)2 * 30

Using the properties of an exponent, we have

A number with an exponent of 0 always gives 1

(36)2 * 1

(3)6×2 * 1

312 * 1

312

Thus, the total number of candies in the store is 312.

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Given:

A student says that the graph of the equation \(y = 3(x + 8)\) is the same as the graph of \(y = 3x\), only translated upwards by 8 units.

To find:

Whether the student is correct or not.

Solution:

Initial equation is

\(y=3x\)

\(f(x)=3x\)

Equation of after transformation is

\(y=3(x+8)\)

\(g(x)=3(x+8)\)

Now,

\(g(x)=f(x+8)\)      ...(i)

The translation is defined as

\(g(x)=f(x+a)+b\)        ...(ii)

Where, a is horizontal shift and b is vertical shift.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

From (i) and (ii), we get

\(a=8\text{ and }b=0\)

Therefore, the graph of \(y=3x\) translated left by 8 units. Hence, the student is wrong.

The number of the students should be sampled to be within 0.25  alcoholic drinks of population mean with 95% probability is 62.

α is the result of subtracting one from confidence interval as well as dividing by two.

α =  (1 - 0.95) ÷ 2 = 0.25

Find z in the Z-table because z does have a p-value of 1 - α.

As a result, the p-value of z is  (1 - 0.025) = 0.975.

Thus, z  = 1.96

Now find M as;

M = z × (σ ÷ √n)

In which,

When M = 1,

The standard deviation, in accordance with the question, is approximately 1.

σ = 1

M = z × (σ ÷ √n)

0. 25 = 1.96 × (1 ÷ √n)

√n = 1.96 × (1 ÷ √n)

Squaring both sides,

(√n)² = ((1.96 × 1) ÷ 0.25)²

n = (7.84)²

n = 61.4656

n ≈ 62

Thus, the number of the students should be sampled to be within 0. 25 alcoholic drink of population mean with 95% probability is 62.

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Answer: 66.70

Step-by-step explanation:

8 2/25 times 16 2/3 then divide by 2 and you get 66.70 will be blue  

This is the right response: T F- F.

What is the explanation:

If the answer to the following question is p, then 2 + 2 = 4.

which is accurate, meaning that this statement has a truth value of True.

The following assertion q illustrates q: 7 + 1 Equals 7.

This is untrue, making the statement's truth value Untrue

As far as we are aware, "pq (p implication q)" means that the truth value of the implication is False only when the truth value of statement p is True.

The truth table reveals that the truth value of pq will be False

So T F → F

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To convert 12 m/s to get a kilometer per minute, we will need to multiply 12m/s by 1000 km/60 m.

Unit conversion is the expression of the same function in a new unit of measurement. Time, for example, can be stated in minutes rather than hours, and distance can be translated from miles to kilometers/feet, or another length measurement. A conversion factor is a numerical equation that allows for the equal conversion of feet to another dimensional analysis unit.

A conversion factor is a number that is used to multiply or divide one set of units into another. When converting to an equivalent value, the proper conversion factor must be utilized. For example, to translate inches to feet, the correct conversion value is 12 inches equals 1 foot. The converting value for minutes to hours is 60 minutes equals 1 hour.

From the information given:

To convert 12 m/s to get a kilometer per minute, we will need to multiply 12m/s by 1000 km/60 m.

The conversion factors are:

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Answer:

I think it's -2

Step-by-step explanation:

Answer:

−10r +10

Step-by-step explanation:

Let's simplify step-by-step.

−5−5r+10−5−5r+10

=−5+−5r+10+−5+−5r+10

Combine Like Terms:

=−5+−5r+10+−5+−5r+10

=(−5r+−5r)+(−5+10+−5+10)

=−10r+10

Answer:

−5r+5

Step-by-step explanation:

To answer this question we will set and solve a system of equations.

Let A be the speed (in miles per hour) of the airplane in still air, and W be the wind speed (in miles per hour).

Since the airplane flying with the wind takes 4 hours to travel a distance of 1200 miles and flying against the wind takes 5 hours to travel the same distance, then we can set the following equation:

Dividing the first equation by 4 we get:

Subtracting A from the above equation we get:

Substituting the above equation in the second one we get:

Simplifying the above result we get:

Adding 1500 to the above equation we get:

Dividing the above equation by 10 we get:

Finally, substituting A=270 at W=300-A we get:

Answer:

The speed of the airplane in still air is 270 miles per hour.

The wind speed is 30 miles per hour.

A woman 5-feet tall casts an 8-foot shadow. at the same time of day, the shadow of a tree nearby is 120 feet long. in feet, 75 feet  tall is the tree.

Let the tree height = x

From the question, we have

5/8 = x/120

x = (5*120)/8

x = 75 feet

Tree height = 75 feet

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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The variable "middle" in a binary search algorithm represents the index or position of the element that is being compared in each iteration of the search process.

In a binary search, the algorithm repeatedly divides the search space in half by comparing the middle element with the target value. The "middle" variable keeps track of the index or position of the element that is considered as the midpoint of the current search range.

During each iteration, the algorithm compares the target value with the element at the middle position. If the target value is equal to the middle element, the search is successful, and the algorithm returns the index of the middle element. If the target value is less than the middle element, the search continues on the left half of the search range, excluding the middle element. If the target value is greater than the middle element, the search continues on the right half of the search range, again excluding the middle element.

The "middle" variable is crucial in the binary search algorithm as it helps determine the boundaries of the search range for each iteration. By updating the middle position based on the comparison results, the algorithm efficiently reduces the search space in each step, resulting in a significant improvement in the search time compared to linear search algorithms.

Thus, the "middle" variable in a binary search algorithm represents the index or position of the element that serves as the midpoint of the current search range, allowing for efficient and systematic exploration of the search space.

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Answer:

x=-72/11 y=-48/11

Step-by-step explanation:

yw !

The exact cost of producing 73rd food processor is 7793.4 AED.

We are given the function to calculate the cost of producing x food processors. C(x)=2100+70x+0.3x²Now, we need to find the exact cost of producing 73rd food processor.

Therefore, we need to substitute x=73 in the given function to calculate the cost of producing the 73rd food processor. C(73) = 2100 + 70(73) + 0.3(73)²C(73) = 2100 + 5110 + 0.3(5329)C(73) = 7793.4.

Therefore, the exact cost of producing 73rd food processor is 7793.4 AED.

Cost typically refers to the amount that a buyer will spend rather than the amount that a seller is asking for, whereas price typically refers to the amount of money that a seller is asking for something.

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When President Dwight Eisenhower ordered the Arkansas National Guard into service to enforce court orders to desegregate schools, it was an example of a) executive orders.

Executive orders are directives issued by the President of the United States that have the force of law. They are used to manage and govern the operations of the federal government. In this case, President Eisenhower used his executive authority to deploy the Arkansas National Guard to enforce the desegregation of schools as mandated by the courts.

The Supreme Court's landmark decision in Brown v. Board of Education in 1954 declared that segregation in public schools was unconstitutional. However, resistance to desegregation persisted in some areas of the country, including Arkansas. To ensure compliance with the court's ruling, President Eisenhower exercised his executive power and deployed the National Guard to Little Rock, Arkansas, to protect and enforce the rights of African American students seeking to attend previously all-white schools.

Therefore, President Eisenhower's action of ordering the Arkansas National Guard to enforce court orders to desegregate schools falls under the category of a) executive orders, as he used his executive authority to implement a policy decision.

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Answer:

$468.16

Step-by-step explanation:

answer key

Based on the representation on the scatter plot, the predicted score of the student in quiz 2 is 67.5

The graph that completes the question is added as an attachment

From the question and the scatter plot of the graph, we have the following parameters:

From the attached graph, we have the following observations

When the points scored on quiz 1 is 65, the points scored on quiz 2 are between 65 and 70

The average of these scores is

Average = 1/2 * (65 + 70)

Evaluate the sum

So, we have

Average = 1/2 * 135

Evaluate the product

So, we have

Average = 67.5

Hence, the score of the student in quiz 2 is 67.5

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In probability theory, a Venn diagram is a diagrammatic representation of sets that shows all possible logical relations between them. Venn diagrams are widely used in probability and statistics to visualize the relationship between different sets of data.

The given Venn diagram shows the relationship between three sets, A, B, and C. In order to calculate probabilities using a Venn diagram, we need to know the number of elements or members in each set, as well as any overlapping regions.

We can then use these numbers to calculate the probability of different outcomes.Let's consider two possible probabilities from the given Venn diagram:1.

The probability that an element is in set A and set B but not in set C is 0.1/0.5 = 0.22. The probability that an element is in set B or set C but not in set A is 0.2/0.6 = 1/3The first probability can be calculated by dividing the number of elements in the overlapping region of sets A and B (which is 0.1) by the total number of elements in set B (which is 0.5).

This gives us a probability of 0.22 or 22%.The second probability can be calculated by dividing the number of elements in the union of sets B and C (which is 0.2) by the total number of elements in either set B or set C (which is 0.6). This gives us a probability of 1/3 or approximately 33%.

Therefore, the correct probabilities are:1.

The probability that an element is in set A and set B but not in set C is 0.1/0.5 = 0.22.

The probability that an element is in set B or set C but not in set A is 0.2/0.6 = 1/3

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Using the points A(3,1) B(3,4) C(-4,1) D(-4,5) the following deductions are made

slope of (line AB): undefined

slope of (line CD) undefined

type of line parallel lines

The slope, m of the linear function is calculated using the points A(3,1) and B(3,4)

m = (y₀ - y₁) / (x₀ - x₁)

m = (1 - 4) / (3 - 3)

m = (-3) / (0)

m = undefined

The slope, m of the linear function is calculated using the points C(-4,1) and D(-4,5)

m = (y₀ - y₁) / (x₀ - x₁)

m = (1 - 5) / (-4 - (-4))

m = (-4) / (0)

m = undefined

The slope ae equal and undefined hence they are vertical parallel lines

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To solve this question, we need to consider the two steps: transferring a student from the second class to the first class, and then randomly choosing a student from the first class.

Let's calculate the probabilities step by step:

Step 1: Transferring a student from the second class to the first class

The probability of transferring a boy from the second class is the ratio of the number of boys in the second class (13 boys) to the total number of students in the second class (13 boys + 12 girls).

P(boy transferred) = 13 / (13 + 12) = 13 / 25

Step 2: Randomly choosing a student from the first class

After the transfer, the first class will have 10 boys and 11 girls. The probability of randomly choosing a boy from the first class is the ratio of the number of boys in the first class (10 boys) to the total number of students in the first class (10 boys + 11 girls).

P(boy chosen from first class) = 10 / (10 + 11) = 10 / 21

Now, to find the overall probability, we multiply the probabilities of the two steps:

P(boy chosen) = P(boy transferred) * P(boy chosen from first class) = (13/25) * (10/21)

Therefore, the probability that the student chosen from the first class is a boy is (13/25) * (10/21), which can be simplified or approximated as needed.

LaTeX code snippet for the answer:

The probability that the student chosen from the first class is a boy is

\($\left(\frac{13}{25}\right) \times \left(\frac{10}{21}\right)$.\)

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No, the first 5 people to arrive at a town meeting is not a random sample of the town's residents.

A random sample is a subset of a population that is selected in a way that gives each member of the population an equal chance of being selected. In this case, the first 5 people to arrive may not be representative of the entire population, as they may not have been selected randomly, and their arrival at the meeting may have been influenced by factors such as their proximity to the meeting place, their level of interest in the topic, or their schedule. A more structured method of selection, such as random digit dialing or door-to-door visits, would be necessary to obtain a random sample of the town's residents.

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Answer:

He made $20 from the 100 stocks combined not each individual stock

Step-by-step explanation:

After simplifying, your solution would be \(x^{2}-5x+4\).

Hope this helps! If not, feel free to comment below and I'll see what I can do to help you. Thanks and good luck!