A projector is connected to your computer and projects onto a large wall. The projector enlarges what is on your computer screen by a scale factor of 325%. An image on your computer is inches long. What is the length of the projected image on your wall?

The triangle AEC is a right angled triangle.

A triangle is a three-sided polygon that consists of three edges and three vertices.

To prove that triangle AEC is a right angled triangle, we need to show that the angle at vertex E is a right angle (i.e., measures 90 degrees).

BD≅CD

we can say that angle BDC is approximately equal to angle CBD.

∠ABD=∠ACD  since they are opposite angles.

AB≅AC

∠ABC =∠ACB.

Therefore, angles ABD and ACD are also approximately equal to angle BAC.

we can say that angle

∠BAC=∠ ABC,

which means that angle EAC is approximately equal to angle ECB.

∠EAC and ∠ ECB add up to approximately 90 degrees

we can say that the angle at vertex E measures approximately 90 degrees.

Therefore, we have shown that triangle AEC is a right angled triangle.

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Using the inequality 38+4x≤61 shown to represent the situation, based on the solution that x ≤ 5.75, the true statement is A. Sam went on at most 5 rides.

Inequality is an algebraic statement showing that two or more mathematical expressions are unequal.

Inequalities are represented as:

The total amount Sam has to spend at the amusement park = $61

The entrance fee = $20

The unit cost of a game = $3

The unit cost of a ride = $4

The total number of games Sam plays = 6

The amount spent on games = $18 ($3 x 6)

The total known cost = $38 ($20 + $18)

Let the number of rides Sam goes on = x

38 + 4x ≤ 61

Thus, the correct statement about the inequality is Option A.

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The size for a TV is determined as the diagonal length of the Television.

The Televisions that we see in our daily life are mostly of the rectangular shape.

A rectangular shape is a shape that has 4 sides in it, the opposite sides of the rectangular are parallel and equal. Two pairs of equal sides are formed in this type of shape.

If we connect the vertices that are directly opposite to each other than it is known as the diagonal of the rectangle . Often we see that the TV is of 32'' or 64''. This only means that the diagonal length of the TV is 32'' or 64''. This is how we measure the size of the TV.

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Answer:

x = 5, y = 2

Step-by-step explanation:

    x - 5.2y = -5.4

+ (-x + 4.3y = 3.6)

-------------------------

         -0.9y = -1.8

                   y = 2

x - 5.2(2) = -5.4

x - 10.4 = -5.4

x = 5

The addition (elimination) method is a good choice for solving this system  because the x's are already opposites, and will cancel out when the two equations are added together. If one was to solve for x first, this method wouldn't be as good of a choice since it involves extra steps to eliminate the y's from the equation.

The perimeter of the triangle is the sum of the lengths of all three sides. Therefore, the expression for the perimeter is:

(10f + 6) + (2f-4) + (9g + 1)

Simplifying the expression:

= 12f + 9g + 3

Therefore, the expression for the perimeter of the triangle is 12f + 9g + 3 centimeters.

Answer:

Step-by-step explanation: I'm not gonna give you the answer but i will explain what you need to do. First you need to draw a bar diagram and then you need to put the number equally. But first in part A is an easy question you only need to explain or tell the steps that you will do to solve the problem. For part C you only need to tell the answer but it says how how many got to fill equally so that means that there are gonna be equal number and an not so equal number. I hope this help you with your answer

If you are trying to find the missing measures of a rectangle, you should know that all rectangles have four sides, and each side has a length.

In other words, if you have a rectangle, two of the angles must be 90 degrees, and the other two angles must also be 90 degrees. To find the missing measures of a rectangle, you need to use the properties of rectangles.

First, find the length of each side. The length of all sides of a rectangle should be the same. Then, calculate the area of the rectangle. You can do this by multiplying the length of one side with the length of the other side.

Finally, you can use the Pythagorean Theorem to find the missing measures.

The Pythagorean Theorem states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

Using this theorem, you can find the length of the hypotenuse of the rectangle.

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Complete Question:

if each quadrilateral is given, then define the steps to find the missing measures a rectangle.

answer : x(2)x(-3--6)

The interpretation of the slope in the context of the problem is: For every hour the electrician works, her pay will increase $28.

The slope of any function is the unit rate or average rate of change of the given function for that situation.

here, we have,

Given the function, E(x) = 130 + 28x, where:

E(x) is the amount an electrician charges per job

130 is the flat rate service which is the starting value or y-intercept

28 is the unit rate or slope, which is the fee charged per hour by the electrician to complete a job.

Thus, the interpretation of the slope in the context of the problem is: For every hour the electrician works, her pay will increase $28.

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The distance between two cities are 7000 miles apart.

What is distance ?

Distance is the amount of space between two points or objects. In the context of the question you asked earlier, "distance between two cities" refers to the actual physical distance between the two cities in terms of miles.

Given by the question:
On the map, 500 miles is represented by each 0.5 inches. Therefore, 1 inch represents 1000 miles.

So, the distance between the two cities on the map is 7 inches. This corresponds to a real-world distance of:

distance on map / scale on map = actual distance

7 inches * 1000 miles/inch = 7000 miles

Therefore, the two cities are 7000 miles apart.

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The vertex form equation is illustrated below.

Directrix (d): The directrix is the horizontal line y = -2.

Focus (F): The focus is the point (0, 2).

Vertex (V): The vertex is the point (0, 0).

Equation: The equation of the parabola is y = 1/4x^2.

The vertex form of a parabola is given by y = a(x-h)^2 + k, where (h, k) is the vertex. We already know the vertex of this parabola, which is (0, 0). To find the value of a, we can use the fact that the distance between the focus and the vertex is equal to the distance between the directrix and the vertex.

The distance between the focus (0, 2) and the vertex (0, 0) is 2 units. The distance between the directrix y = -2 and the vertex (0, 0) is also 2 units. Therefore, we can say that 1/(4a) = 2, or a = 1/8.

So, the vertex form equation of the parabola is y = 1/8(x-0)^2 + 0, which simplifies to y = 1/8x^2.

Vertex: The vertex is (0, 0).

Axis of Symmetry (AOS): The axis of symmetry is the vertical line x = 0.

Domain: The domain of the parabola is all real numbers, because the parabola continues indefinitely in both directions along the x-axis.

Range: The range of the parabola is y >= 0, because the lowest point on the parabola is the vertex (0, 0).

Transformations: The only transformation applied to the basic parabola y = x^2 is a vertical compression by a factor of 1/8.

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Answer: The tape diagram that represents the problem is the second (7/3)

Step-by-step explanation:

3/7 isn't 7/3, and 7/7 isn't 7/3. By process of elimination, the second answer works; 7/3 = 7/3.

Slice a cylinder so that the cross section is parallel to the bases. The cross section is rectangular in form.

A cylinder's cross-section, for instance, is a circle when it is cut parallel to the base. The cross-sectional area of this slice is therefore equal to the area of a circle whose radius is the same as the radius of the cylinder supplied.

The cross-section has a rectangular form. It is identical in size and form to the base. We will now cut it with a plane that is parallel to the base. Keep in mind that perpendicular lines cross the base at  ninety degrees.

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Answer:

Step-by-step explanation: Yes, but ONLY when you are multiplying or dividing.

Answer:

Step-by-step explanation:

Therefore , the solution of the given problem of area comes out to be

the actual area of the basketball court is 4,700 square feet.

Its surface area is a reliable indicator of its overall size. When figuring out the right triangle's squared, the environment is taken into account. The surface area of everything determines its overall size. The total of the volumes from each of the twelve vertical sides makes up the water volume inside a cuboid. Utilize the following formula to get the box's dimensions: The region is represented by 2lh, 2lw, & 2hW. (SA). The area is represented by the flexible shape's entire surface area.

Here,

First, let's find the length and width of the basketball court in feet using the scale:

Length = 1 inch on the drawing represents 8 feet in reality

Length of the drawing = 11.75 inches

Actual length = 8 feet/inch × 11.75 inches = 94 feet

Width = 1 inch on the drawing represents 8 feet in reality

Width of the drawing = 6.25 inches

Actual width = 8 feet/inch × 6.25 inches = 50 feet

Now, we can find the actual area of the basketball court:

Actual area = Actual length × Actual width

Actual area = 94 feet × 50 feet

Actual area = 4,700 square feet

Therefore, the actual area of the basketball court is 4,700 square feet.

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A line's slope might be zero, positive, negative, or undefinable. The slope of a horizontal line is zero because it does not climb vertically (y1 y2 = 0), but the slope of a vertical line is unknown because it does not run horizontally (x1 x2 = 0).

The slope (m = 3.5 is positive) and y-intercept (b = 4) of the line y = 3.5x + 4 are both positive. This indicates that the y-intercept, or point (0, 4), is where the line crosses.

A line on a plane with no upward or downward slope is known as a line with zero slope in mathematics and computer science.

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The superposition is the imposing of one wave on the other and resulting in the change of the amplitude of the final wave.

When two or more waves travel through the same space in superposition, their combined amplitudes equal the amplitudes they would have produced individually. For instance, two waves moving in the same direction will pass through each other without causing any distortion on the other side.

The pattern you see when shining light through two slits, the sounds you hear in acoustically sound rooms and music halls, the interference radios receive when moved close to other electronic devices, and any tone produced by a musical instrument are all examples of the superposition principle in action.

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To calculate the optimal bundle, you need to find the combination of goods or services that maximizes the consumer's utility while staying within their budget constraint.

The optimal bundle can be found by using the consumer's utility function and their budget constraint. The utility function specifies how much utility the consumer gets from consuming various quantities of the goods or services, while the budget constraint specifies the combinations of goods or services that the consumer can afford given their income and the prices of the goods or services.

To find the optimal bundle, follow these steps:

Write down the consumer's utility function, such as U(x, y) where x and y are the quantities of two goods.

Write down the consumer's budget constraint, such as P_x x + P_y y = I where P_x and P_y are the prices of the goods, I is the consumer's income, and x and y are the quantities of the two goods.

Find the marginal utility of each good by taking the partial derivative of the utility function with respect to each good. For example, the marginal utility of x is given by dU/dx.

Set the marginal utility per dollar spent on each good equal to each other, since the consumer should allocate their spending so that the marginal utility per dollar spent is the same for both goods. That is, set dU/dx / P_x = dU/dy / P_y.

Solve the resulting equations for the quantities of the goods that maximize the consumer's utility subject to their budget constraint.

The resulting combination of goods that solves the optimization problem is the consumer's optimal bundle. It represents the combination of goods that maximizes the consumer's utility given their budget constraint.

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The possible outcomes for flipping a two-sided tile once are:

Toss 1 Toss 2 Toss 3

Black Black Black

Black Black White

Black White White

Black White Black

White White White

White White Black

White Black Black

White Black White

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Now, If we flip the tile three times, the sample space will consist of all possible outcomes of the three flips.

Hence, Each flip is independent, so the total number of possible outcomes is the product of the number of outcomes for each flip, which is 2.

Therefore, the sample space for flipping the tile three times is:

BBB,

BBW,

BWB,

BWW,

WBB,

WBW,

WWB,

WWW

Where,

B = the black side facing up, and

W = the white side facing up.

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The characteristics of a data set are enumerated by descriptive statistics. You can test a hypothesis or determine whether your data can be applied to a larger population by using inferential statistics.

To summarize a given data set, which may be a sample of a population or a representation of the entire population, brief informational coefficients known as descriptive statistics are used.

The two primary subcategories of descriptive statistics are measures of central tendency and measures of variability (spread). Descriptive statistics are thus used to summarize the data. Descriptive statistics can only ever make claims about the data set from which they were derived, using only the data that you have.

Statistical inference is the process of determining characteristics of an underlying probability distribution through the use of data analysis. Inferential statistical analysis, for instance, infers characteristics of a population by testing hypotheses and producing estimates.

Inferential statistics looks to identify some characteristic or overarching pattern about a large group through the study of a smaller sample size in the hopes that the results will apply to the larger group.

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The answer choice which is most appropriate to describe the center of the data as represented is; Median.

It follows from the task content that the stemans leaf plot shown in the task content is such that;

It contains outliers such as 5.1 and 4.2 and hence, the median best appropriates the central of the data distribution as it is minimally influenced by the extremes of data.

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Attribute that describes right pyramid is triangular faces.

A pyramid is a three-dimensional shape. A pyramid has a polygonal base and a flat triangular face that join at a common point called the apex. A pyramid is formed by connecting the base and apex. Each edge of the base connects to the top and forms triangular faces called sides.

Given, properties of right pyramid

1. 2 apexes - A right pyramid has only one apex

2. Triangular faces - A right pyramid has flat triangular faces.

3. Circular base - A right pyramid has polygonal base, not circular base

4. curved surface - A right pyramid has flat surface, not curved surface.

Hence, Property of triangular faces is present in a right pyramid.

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Number of people were invited on Friday is 2^3 = 8 and  the value of the power is 3

Let's track the number of invitations over the course of the week:

Monday: 2 invitations

Tuesday: Each of the 2 friends invited 2 more friends, for a total of 2 x 2 = 4 invitations

Friday: Each of the 4 friends invited 2 more friends, for a total of 4 x 2 = 8 invitations

So on Friday, there were a total of 8 invitations. We can write this as 2^3, since we started with 2 invitations and multiplied by 2 three times (once for each round of invitations). Therefore, the value of the power is 3.

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Answer:

0.06

Step-by-step explanation:

Identify the probability to the nearest hundredth that a point chosen randomly inside the rectangle either is in the hexagon or in the circle

Area of rectangle = 26.2 * 13 =  340.6 sq inch

Area of Hexagon  = 3√3(side)²/2 = 3√3 (1.8)²/2 = 8.42 sq inch

Area of circle = π(radius)² = 3.14 * (2)² = 12.56 sq inch

Area of hexagon + area of circle = 12.56 + 8.42 = 20.98 sq inch

Probability of selecting point inside the hexagon or in the circle  = 20.98/340.6

= 0.06

Answer:

Look at the screenshot

Step-by-step explanation:

Rounding to the nearest square unit, the area is approximately 21 square units.

A quadrilateral is a polygon with four sides, four vertices (corners), and four angles. Some examples of quadrilaterals include rectangles, squares, parallelograms, trapezoids, and rhombuses. Quadrilaterals can have sides and angles of different lengths and sizes. However, the sum of the angles in a quadrilateral always adds up to 360 degrees. Quadrilaterals are commonly studied in geometry, where their properties and characteristics are analyzed and used to solve various problems related to area, perimeter, and other geometric concepts.

Here,

To find the area of the figure ABCE, we need to find the height of the triangle ABCE with respect to base AB.

Let's call the point where the height meets base AB as D. Since angle E is 65 degrees, we know that angle AED is 180 - 65 = 115 degrees (since the sum of the angles in triangle AED is 180 degrees).

We also know that angle ADB is a right angle (since AD is perpendicular to AB), so angle EDB is 180 - 115 - 90 = 25 degrees.

Using trigonometry, we can find that the length of AD is:

AD = AB * sin(25) = 10 * sin(25) ≈ 4.24 units.

Therefore, the area of quadrilateral ABCE is:

Area = (1/2) * base * height = (1/2) * AB * AD ≈ (1/2) * 10 * 4.24 ≈ 21.2 square units.

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The lower fence is 56.2428

As the Iq score < lower fence,   Iq score is outlier

What is average/mean?

The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics. When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.

data was collected from 221 children

iq scores at age of 7  approximately follow a normal distribution with mean of 87.0 and standard deviation of 11.4.

Let X=iq scores

distribution is

X ~ [tex]N( \mu=87, \sigma=11.4)[/tex]

If one child has iq of 55,

To find outlier, find the lower fence

lower fence = [tex]Q_{1}-1.5( Q_{3} - Q_{1} )[/tex]

[tex]Q_{1} = \mu + Z_{0.25}\sigma[/tex]

[tex]Q_{3} = \mu + Z_{0.75}\sigma[/tex]

Using excel function,

[tex]Z_{0.25} = -0.67[/tex]

[tex]Z_{0.75} = 0.67[/tex]

[tex]Q_{1} = \mu + Z_{0.25}\sigma[/tex]

    =87+(-0.6745)11.4

   = 79.3107

[tex]Q_{3} = \mu + Z_{0.75}\sigma[/tex]

    = 87+(0.6745)11.4

   = 94.6893

lower fence = [tex]Q_{1}-1.5( Q_{3} - Q_{1} )[/tex]

                    = 79.3107 -1.5(94.6893 - 79.3107 )

                    = 56.2428

So, the  lower fence is 56.2428

As the Iq score <  lower fence,   Iq score is outlier

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