The midpoint of AB is =M−−6, 2. One endpoint is =A−−8, 7. Find the coordinates of the other endpoint, B

Smallest number in the data set that is not an outlier is 15, Median of the first half is 17, Median of the entire data set is 20.5. Median of the second half is 22. Largest number in the data set that is not an outlier is 35.

Give a short note on Median?

In statistics, the median is a measure of central tendency that represents the middle value in a dataset. To find the median, the data must first be sorted in ascending or descending order. If the dataset contains an odd number of values, the median is the middle value. If the dataset contains an even number of values, the median is the average of the two middle values.

The median is a useful measure of central tendency in datasets that are skewed or have outliers, as it is less sensitive to extreme values than the mean. It is also useful in datasets with non-numeric values, such as rankings or survey responses.

To create a modified box plot, we need the following values:

The smallest number in the data set that is not an outlier: 15

The median of the first half of the data set: 17

The median of the entire data set: 20.5

The median of the second half of the data set: 22

The largest number in the data set that is not an outlier: 35

So the values needed to create a modified box plot for this data set are: 15, 17, 20.5, 22, 35.

Answer:

576 books.

Step-by-step explanation:

134+254+188=576 books in total.

Answer:

576

Step-by-step explanation:

This is literally easy!

Checked books are 134 + 254 + 188 = 576

Answer:

To find the area of the given figure, we can divide it into two separate shapes, a rectangle and a triangle, and then add their areas together.

First, we can find the area of the rectangle by multiplying its length and width. From the diagram, we can see that the length of the rectangle is 12 cm and the width is 5 cm.

Area of rectangle = length x width

Area of rectangle = 12 cm x 5 cm

Area of rectangle = 60 cm^2

Next, we can find the area of the triangle by using the formula for the area of a triangle, which is:

Area of triangle = 1/2 x base x height

From the diagram, we can see that the base of the triangle is 5 cm and the height is 8 cm.

Area of triangle = 1/2 x base x height

Area of triangle = 1/2 x 5 cm x 8 cm

Area of triangle = 20 cm^2

Finally, we can find the total area of the figure by adding the area of the rectangle and the area of the triangle:

Total area = area of rectangle + area of triangle

Total area = 60 cm^2 + 20 cm^2

Total area = 80 cm^2

Therefore, the area of the given figure is 80 square centimeters.

Step-by-step explanation:

The area of the circle will decrease by 51% if the diameter increases by 40%. Then the new diameter will be 1.4 times the original diameter.

Let's assume the original diameter is d and the original area of the circle is A.

Then, the new diameter will be 1.4d and the new area of the circle can be calculated as follows:

New area = pi * (New diameter/2)²= pi * (1.4d/2)² = pi * (0.7d)² = 0.49 * pi * d²

Therefore, the new area is 0.49 times the original area.

To calculate the percentage increase in area, we can use the following formula:

Percentage increase = (New value - Old value) / Old value * 100%

In this case, the old value is the original area A and the new value is the new area, which is 0.49*A. Therefore,

Percentage increase = (0.49A - A) / A * 100%

= -0.51A / A * 100%

= -51%

Therefore, the area of the circle will decrease by 51% if the diameter increases by 40%.

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Answer:

3c + 19

Step-by-step explanation:

Perimeter: P = a + b + c

P = (c + 10) + (c + 6) + (c + 3) = 3c + 19

In the equation A’ = 364V relating the surface area A and the volume V of a spherical balloon. We are also given that the volume is increasing at a rate of 18 cubic inches per second.so the rate at which the surface area of the balloon is increasing is 6552 square inches per second

We want to find the rate at which the surface area is increasing when A = 153.24 square inches and V = 178.37 cubic inches.

To find the rate of change of A with respect to time, we can use the chain rule of differentiation:

dA/dt = dA/dV × dV/dt

We know that dV/dt = 18 cubic inches per second, so we just need to find dA/dV and then we can find dA/dt.

To find dA/dV, we differentiate the equation A’ = 364V with respect to volume V:

dA/dV = 364

Now we can find dA/dt:

dA/dt = dA/dV × dV/dt ⇒ 364 × 18 ⇒ 6552 square inches per second

So the rate at which the surface area of the balloon is increasing is 6552 square inches per second when A = 153.24 square inches and V = 178.37 cubic inches.

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The dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 19 in. by 11 in. by cutting congruent squares from the corners and folding up the sides are 6.33 in. x 3.33 in. x 5.33 in. The volume of the box is 113.78 in³.

The dimensions of the box can be found with the following steps:

First, determine the side length of the square that is to be removed from each corner of the cardboard box. Since this will be done uniformly on all four corners, let the side length be x. The dimensions of the cardboard box can then be written as:

Length = 19 in. - 2x

Breadth = 11 in. - 2x

Height = x

After folding the cardboard along the creases, the base of the rectangular box will be (19 - 2x) in. by (11 - 2x) in. with the height of the box being x in. The volume of the box can then be found by multiplying the base and height of the box, i.e.,

Volume = (19 - 2x) (11 - 2x) x

Let V(x) be the volume of the rectangular box in terms of x. Then:

V(x) = (19 - 2x) (11 - 2x) x

Simplifying,

V(x) = 4x³ - 60x² + 209x

The maximum value of V(x) can be found by differentiating V(x) with respect to x and equating the result to zero. Therefore,

V'(x) = 12x² - 120x + 209 = 0

Solving, V(x) has a maximum value when x = 19/3 - 2(2/3)√14 or x = 19/3 + 2(2/3)√14. The value x = 19/3 - 2(2/3)√14 is the maximum value because x must be less than 5.5, which is the minimum of 11/2 and 19/2 divided by 3, the upper bound for x. Therefore, the dimensions of the box are

Length = 19 - 2(19/3 - 2(2/3)√14) = 6.33 in.

Breadth = 11 - 2(19/3 - 2(2/3)√14) = 3.33 in.

Height = 19/3 - 2(2/3)√14 = 5.33 in.

Thus, the dimensions of the box are 6.33 in. x 3.33 in. x 5.33 in. The volume of the box is:

V = 6.33 x 3.33 x 5.33 = 113.78 in³.

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The total resistance of the circuit is  6 + 2i.

Resistance is a unit of measurement for the resistance to current flow in an electrical circuit. The Greek letter omega () represents the unit of measurement for resistance, which is ohms.

Georg Simon Ohm (1784–1854), a German physicist who investigated the connection between voltage, current, and resistance, is the name given to the unit of resistance known as an ohm.

The amount of opposition any object applies to the flow of electric current is known as resistance. A resistor is an electrical component utilised in the circuit to provide that particular level of resistance. R = V I is a formula used to calculate an object's resistance.

given :

R1 =  (4 + 6i)

R2 = (2 - 4i)

total resistance of the circuit is

R = R1 + R2

= (4 + 6i) + (2 - 4i)

= 6 + 2i

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The equation RT = + R1 = 4 + 6i ohms and R2 = 2 4i ohms, RT = 6 - 2i ohms, determines the circuit's total resistance.

R1 and R2 are added to determine RT: RT = R1 + R2.

The actual components added together give us 4 + 2 = 6.

When we add the fictitious parts, we obtain 6i - 4i = 2i.

RT is thus equal to 6 - 2i ohms.

To put it another way, the circuit's total resistance is a complex number containing a real component of 6 ohms and an imaginary component of -2 ohms. This shows the combined impact of the circuit's resistances R1 and R2. When a constant voltage differential of one volt (V) is supplied to two conductor points and a current of one ampere (A) results, the resistance between those points is measured in ohms. It is comparable to one volt for every ampere (V/A), to put it simply.

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Net rendering is a method of rendering a computer-generated animation or image on multiple computers over a network.

Net rendering is a method of rendering a computer-generated animation or image on multiple computers over a network. This technique allows a user to take advantage of the computing power of multiple computers to render a scene. To do this, the user would divide the scene into several parts, assigning each part to a different computer. The computers would then render each part of the scene independently, and then the results are combined into a single image. This process can significantly reduce the time required to render a scene, as the workload is distributed over multiple computers. For example, if it would normally take a single computer 10 minutes to render a scene, net rendering could reduce that time to 2 minutes.

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Answer: 4 batches of fudge brownies and 1 batch of peanut butter brownies were made.

Step-by-step explanation:

Let x be the number of batches of fudge brownies made, and y be the number of batches of peanut butter brownies made.

From the problem, we can write two equations based on the information given:

   Each batch of fudge brownies makes 1 pan: x = number of pans of fudge brownies.

   Each batch of peanut butter brownies makes 9 pans: 9y = number of pans of peanut butter brownies.

We also know that the class made 5 batches in total, and ended up with 29 pans:

x + 9y = 29 (total number of pans)

We can now solve for x and y by using a system of two equations:

x + 9y = 29 (equation 1)

x + y = 5 (equation 2)

Solving for x in equation 2 and substituting into equation 1, we get:

(5 - y) + 9y = 29

Simplifying and solving for y:

8y = 24

y = 3

Substituting y = 3 into equation 2, we get:

x + 3 = 5

x = 2

Therefore, the class made 2 batches of fudge brownies (2 pans) and 1 batch of peanut butter brownies (9 pans), for a total of 29 pans. Alternatively, we can say that the class made 4 batches of fudge brownies (4 pans) and 1 batch of peanut butter brownies (9 pans) for a total of 29 pans.

Answer: 100:3

Step-by-step explanation:

Answer:

the ratio of first-year college basketball players to high school seniors playing basketball is 3:100.

Step-by-step explanation:

The problem states that for every 75,000 high school seniors playing basketball, about 2,250 play college basketball as first-year students. To write the ratio of first-year college basketball players to high school seniors playing basketball, we need to compare the two quantities.

The ratio is a way of expressing the relationship between two numbers as a fraction or a pair of numbers separated by a colon (:). In this case, we want to express the ratio of the number of first-year college basketball players to the number of high school seniors playing basketball.

To write the ratio, we start by putting the number of first-year college basketball players (2,250) in the numerator of a fraction. We put the number of high school seniors playing basketball (75,000) in the denominator of the same fraction.

So the ratio can be expressed as:

2,250/75,000

To simplify this fraction, we can divide both the numerator and denominator by a common factor. In this case, both 2,250 and 75,000 are divisible by 750. Dividing both numbers by 750 gives:

2,250/75,000 = 3/100

We can construct the 95% confidence interval for the true proportion. To do this, we need to calculate the margin of error, which is equal to the critical value (1.96) multiplied by the standard error (0.014). This equals 0.028.

The 95% confidence interval is then the sample proportion (0.38) plus or minus the margin of error (0.028). This is [tex](0.38 - 0.028, 0.38 + 0.028) = (0.352, 0.408).[/tex]

The test statistic in this case is the Z-statistic, as we are assuming that the underlying population is normally distributed. To conduct the hypothesis test, we must first state the null and alternative hypotheses.

Null Hypothesis (H0): The proportion of students at the school who fear public speaking is equal to or greater than 40%.
Alternative Hypothesis (H1): The proportion of students at the school who fear public speaking is less than 40%.

We must then calculate the test statistic, which is the Z-statistic in this case. To do this, we need to first calculate the sample proportion, which is the number of students who fear public speaking (137) divided by the total number of students surveyed (361). This equals 0.38. We then need to calculate the standard error of the sample proportion (SE), which is the square root of [tex](pq/n)[/tex], where p is the sample proportion (0.38) and q is the complement of the sample proportion (1-0.38 = 0.62). SE = [tex](0.38 x 0.62)/361 = 0.014.[/tex] The Z-statistic is then calculated as the difference between the sample proportion (0.38) and the population proportion (0.40) divided by the standard error [tex](0.014). Z = (0.38 – 0.40)/0.014 = -0.14.[/tex]

To conclude, we can use the Z-statistic and 95% confidence interval to test the hypothesis that the proportion of students at the school who fear public speaking is less than 40%. The Z-statistic of -0.14 falls within the critical region and the 95% confidence interval does not include 0.40, suggesting that the proportion of students at the school who fear public speaking is indeed less than 40%.

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It would cost €27 to buy a sheet of area 4 meters by 75 centimeters.

We solve this problem easily by employing the unitary method. To answer this question, we need to first calculate the area of the metal sheet being sold and the area of the metal sheet being purchased.

The area of the metal sheet being sold is:

5 meters × 2 meters = 10 square meters

The area of the metal sheet being purchased is:

4 meters × 0.75 meters = 3 square meters

Now we can calculate the price per square meter of the metal sheet being sold:

€90 ÷ 10 square meters = €9 per square meter

Finally, we can calculate the cost of the metal sheet being purchased:

3 square meters × €9 per square meter = €27. Therefore, the cost to buy a sheet of area 4 meters by 75 centimeters which costs €90 to a metal of area 5 meters by 2 meters would be €27.

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The smallest value of `n` for which `S_n` has an element of order greater than or equal to 100 is 101.

To determine the smallest value of n for which S_n has an element of order greater than or equal to 100, we can use the formula

S_n = n!/r!(n - r)!,

where n is the number of elements in the set, and r is the number of elements being chosen at a time.

Given, S_n has an element of order greater than or equal to 100. The smallest value of n should be determined.

The formula for the number of permutations in a set with n elements is given by, `S_n = n!/r!(n - r)!`

where `n` is the number of elements in the set and `r` is the number of elements being chosen at a time.

The element of order `n` in `S_n` is an `n` cycle. For `n = 100`, we have an element of order 100.

This element can be expressed as `(1 2 3 ... 99 100)`. Thus, `r = 100`.

Substituting these values in the formula of S_n we get, S_n = n!/r!(n - r)! => n!/(100!(n - 100)!)

Now, we have to find the smallest value of n for which S_n has an element of order greater than or equal to 100. If we substitute `n = 100`, then we will have an element of order 100. But the question asks for the smallest value of n. So, if we substitute `n = 101`, we will have an element of order `101`. Hence, the smallest value of `n` for which `S_n` has an element of order greater than or equal to 100 is 101.

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To understand why b = d = 0 if the function is even, we need to consider the definition of an even function.Therefore If P(x) is an even function, then b = d = 0.

A polynomial is a mathematical expression that consists of variables and coefficients, combined using the operations of addition, subtraction, and multiplication. It can have one or more terms and can be of any degree.

An even function is a function that satisfies the condition f(x) = f(-x) for all x in the domain of the function.

If P(x) is an even function, then we have P(x) = P(-x) for all x. Substituting -x for x in the expression for P(x), we get:

P(-x) = a(-x)⁴ + b(-x)³ + c(-x)² + d(-x) + e

= a(x⁴) - b(x³) + c(x²) - d(x) + e

Since P(x) = P(-x), we can equate the two expressions for P(x) and P(-x) to get:

a(x⁴) + b(x⁴) + c(x²) + d(x) + e = a(x⁴) - b(x³) + c(x²) - d(x) + e

Simplifying this equation, we get:

2b(x³) + 2d(x) = 0

Since this equation holds for all values of x, we can set x = 0 to get:

2d(0) = 0

which implies that d = 0. Similarly, setting x = 1, we get:

2b(1³) + 2d(1) = 0

2b = 0

b = 0

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Therefore, the ladder is approximately 8.72 feet away from the house.

Pythagoras' theorem is a fundamental theorem in mathematics that states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In equation form, it can be written as:

c² = a² + b²

where c is the length of the hypotenuse, and a and b are the lengths of the other two sides of the right triangle.

Here,

We can use the Pythagorean theorem to solve this problem. Let x be the distance from the base of the ladder to the house.

In equation form, it can be written as:

c² = a² + b²

where c is the length of the hypotenuse, and a and b are the lengths of the other two sides of the right triangle.

Then we have:

x² + 18² = 20²

Simplifying and solving for x, we get:

x² = 20² - 18²

=400 - 324

= 76

x = √(76)

= 8.72 (rounded to two decimal places)

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In the given system of equations one taco costs $0.80 and one burrito costs $0.72.

An equation system is a finite collection of equations for which we searched for the common solutions. It is sometimes referred to as a set of simultaneous equations or an equation set. The classification of a system of equations is similar to that of a single equation. In modelling issues where the unknown values may be expressed in the form of variables, a system of equations finds use in everyday life.

Let us suppose the cost of one taco = x.

Let us suppose the cost of one burrito = y.

Then, for Emma we have:

3x + y = 3.65

For Cooper we have:

x + 2y = 3.30

Using elimination, multiply the first equation by 2 and subtract it from the second equation:

(2)(3x + y = 3.65)

6x + 2y = 7.30

x + 2y = 3.30

-5x = -4

x = 4/5

Substituting this value of x into either equation:

3(4/5) + y = 3.65

y = 2.15/3 ≈ 0.72

Therefore, one taco costs $0.80 and one burrito costs $0.72.

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Answer:

Step-by-step explanation:

2/5-1 2/5

Answer:

Step-by-step explanation:

= 2(15+8)

=2(23)

=46

Andre can make 6 small cranes. X is the number of small cranes, 3x is the minutes, 10 is the minute for large cranes and 30 is the total time.

3x + 10 is less than or equal to 30

3 is the minutes for the small cranes

X is the number of small cranes

10 is the minutes for the large crane

30 is the total time limit

first, subtract 10 from 30, ( 30-10) which gives you 20 so

3x is less than or equal to 20.

To figure this out, divide 20 by 3, which gives you 6 as a quotient with a remainder of two minutes.

Andre can make 6 small cranes.

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The Complete question is

Andre is making paper cranes to decorate for a party. He plans to make one large paper crane for a centrepiece and several smaller paper cranes to put around the table. It takes Andre 10 minutes to make the centrepiece and 3 minutes to make each small crane. He will only have 30 minutes to make the paper cranes once he gets home.

​Andre wrote the inequality 3x + 10 ≤ 30 to plan his time. Describe what x, 3x, 10, and 30 represent in this inequality.

Solve Andre’s inequality and explain what the solution means.

Answer:

Step-by-step explanation:

Answer:

Solve the problems. a) The number a is 4/5 of the number b. What part of number a is number b?

Step-by-step explanation:

a) If a is 4/5 of b, then b is 5/4 of a.

To find what part of a is b, we divide b by a:

b/a = 5/4

This means that b is 5/4 times larger than a, or b is 125% of a.

To find what part of a is b, we subtract 1 from this fraction:

b/a - 1 = 5/4 - 1

b/a - 1 = 1/4

So, b is 1/4 of a, or b is 25% of a.

Answer:

103

Step-by-step explanation:

57° + 46° =103°

This shows that the third angle in the triangle is 180°-103°=77°

Therefore the largest exterior angle is 180°-77°=103°

Each pair of children gets to bat for 7.5 minutes.

To find out how much time each pair gets to bat, we need to divide the total session time by the number of pairs of children who bat.

Number of pairs of children who bat = 6 groups x 1 pair/group = 6 pairs

Total time for the session = 45 minutes

Time per pair of children who bat = Total time / Number of pairs of children who bat

= 45 minutes / 6 pairs

= 7.5 minutes per pair

Therefore, each pair of children gets to bat for 7.5 minutes.

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If f(x,y) > 0 and is a continuous function defined over a rectangle R=[a,b]x[c,d], then the double integral over R of f(x,y) can be interpreted as the volume of a solid that lies in the first octant and under the graph of the function f(x,y) over the region R.

The geometric interpretation of the double integral over R of f(x,y) if f(x,y) > 0, where f is a continuous function defined on a rectangle R = [a,b] × [c,d] is given as follows:

The double integral of f(x,y) over R, if f(x,y) > 0, gives the volume under the graph of the function f(x,y) over the region R in the first octant.

Consider a point P (x, y, z) on the graph of f(x, y) that is over the region R, and let us say that z = f(x,y). If f(x,y) > 0, then P is in the first octant (i.e. all its coordinates are positive).

As a result, the volume of the solid that lies under the graph of f(x,y) over the region R in the first octant can be found by integrating the function f(x,y) over the rectangle R in the xy-plane, which yields the double integral.

The following formula represents the double integral over R of f(x,y) if f(x,y) > 0:

∬Rf(x,y)dydx

The geometric interpretation of the double integral over R of f(x,y) if f(x,y) > 0 is given by the volume of the solid that lies under the graph of the function f(x,y) over the region R in the first octant.

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To create opposite x terms, we need to multiply the first equation by -5.

How to choose what term to multiply the first equation?

To choose what term to multiply the first equation, we need to consider the coefficients of the variable that we want to eliminate (in this case, the x variable) in both equations. Our goal is to create opposite terms for that variable in the two equations, so that when we add or subtract the equations, that variable will be eliminated.

Determining the number to multiply the first equation by to form opposite terms for the x-variable :

In this case, the coefficient of x in the first equation is 2/5, and the coefficient of x in the second equation is -2.

To create opposite terms for x, we need to find a constant that, when multiplied by the first equation, will result in a coefficient of x that is the negative of the coefficient of x in the second equation (i.e., -2).

To do this, we can divide the coefficient of x in the second equation by the coefficient of x in the first equation, and then multiply the entire first equation by the resulting constant.

In this case, we have:

[tex](-2)/(2/5) = -5[/tex]

Multiplying the first equation by -5 gives:

[tex]-5(2/5)x + (-5)6y = -5(-10)[/tex]

which simplifies to:

[tex]-2x - 30y = 50[/tex]

Now we have two equations with opposite x terms:

[tex]-2x - 4y = 40[/tex]

[tex]-2x - 30y = 50[/tex]

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We can reduce the width of the confidence interval by increasing the sample size, reducing the confidence level and decreasing the mean (A, D, and F)

A confidence interval is an estimate of the interval that has a specified probability of including an unknown population parameter.

The purpose of a confidence interval is to estimate the true value of the population parameter being measured, such as a mean, a standard deviation, or a proportion.

In general, a wider confidence interval indicates more uncertainty about the estimate, while a narrower confidence interval suggests more precision in the estimate.

We want narrower confidence intervals to demonstrate more precision, as this allows us to draw more reliable conclusions about population parameters.

We cannot reduce the width of the confidence interval by increasing the sample size, increasing the confidence level or increasing the mean.

Thus, the correct options are a, d, and f.

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Step 1: x is a positive number, so the absolute value of x will be equal to x.

Step 2: The expression x+|x| simplifies to 2x

Step 3: Therefore, the expression x+|x| = 2x if x≥0

The value of x= 10.2.

This is the boundary or contour length of a 2D geometric shape.

Depending on their size, multiple shapes may have the same circumference. For example, imagine a triangle made up of wires of length L.

The same wire can be used to create a square if all sides are the same length.

The length covered by the perimeter of the shape is called the perimeter. Therefore, the units of circumference are the same as the units of length.

As we can say, the surroundings are one-dimensional. As a result, you can measure in meters, kilometers, millimeters, etc.

Inches, feet, yards, and miles are other globally recognized units of circumference measurement.

Hence, The value of x= 10.2.

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