Luke is designing a scale model of a clock tower. The design of the front of the tower is shown below.

A figure can be broken into a triangle and rectangle. The rectangle has a base of 200 millimeters and height of 50 millimeters. The triangle has a base of 50 millimeters and height of 100 millimeters.

What will be the area of the front face of his model?
2,500 square millimeters
10,000 square millimeters
12,500 square millimeters
15,000 square millimeters

The correct statement is: the volume of the cylinder is 8 cubic inches more than that of the cone.

The volume of cone (V) = 1/3 * πr²h

Volume of cylinder (V) = πr²h

Where, r is the radius of their bases.

The base area formula for the cone = πr²

Calculate the area of the base of the cone that has a radius (r) of 2.5 in:

Area of the base of the cone = π(2.5)² ≈ 19.6

The volume of the cone (V) = 1/3 * πr²h = 1/3 * π * 2.5² * 6.5

≈ 42.5 cubic inches

Volume of cylinder (V) = πr²h = π * 2² * 4

≈ 50.3 cubic inches

The difference in volume = 50.3  - 42.5

= 7.8 ≈ 8 cubic inches

Therefore, the only statement that is true is: the volume of the cylinder is 8 cubic inches more than that of the cone.

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Answer:

Step-by-step explanation:

Height of model = 20 ft ⋅ (2 in)/(5 ft) = 8 in

The following is the least appropriate measure of central tendency for a data set that contains outliers is 2ndquartile.

A single number that seeks to characterise a set of data by pinpointing the centre position within that set of data is referred to as a measure of central tendency. As a result, measures of central location are occasionally used to refer to measures of central tendency. They also fit within the category of summary statistics. You are probably most familiar with the mean (sometimes known as the average), but there are additional central tendency measures, including the median and the mode.

The mean, median, and mode are all reliable indicators of central tendency, however depending on the situation, some indicators are more useful than others.

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A linear expression is in polynomials when it is expressed as the product of it's factor

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1. For example, x² is a variable raised to the second power, but x is a variable raised to the first power.

When two linear factors are expressed together the result forms a polynomial.

A polynomial is an expression in which the power of it's variable is higher than 1. quadratic expression is also an example of polynomial.

For example if an expression is given as (x+2)(x+3). The result of the expression will give x²+5x+6 which is a quadratic expression and a polynomial.

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Answer:

8(34a−1)

Step-by-step explanation:

From the rectangle given, we see the diagonals of the rectangle bisect each other at E.

From the properties of a rectangle is that;

1) The diagonals are congruent. That is, they are equal. AC = BD

2) The diagonals bisect each other into two equal parts.

These are the two properties we will use in solving the question

The graph of the equation y = \(2^{x}\) - 5 is obtained by shifting the graph of

y =\(2^{x}\)  downside by 5 units.

To find a graph of equation y = \(2^{x}\) - 5, we can start with the reference of the parent function y = \(2^{x}\) and also apply the necessary transformations.  Initiating with the graph of the parent function y =\(2^{x}\) - 5.

This is an exponential function that passes through the point( 0, 1) and has a positive pitch. Apply the transformation -5 units over. This means we shift the entire graph over by 5 units. The point( 0, 1) will now come( 0,-4).thus, the graph of the equation y =  \(2^{x}\)- 5 is attained by shifting the graph of y =  \(2^{x}\) downcast by 5 units. The factual shape of the graph will act as that of the parent exponential function, but it'll be shifted over by 5 units.

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The correct question is given below-

Graph the equation shown below by transforming the given graph of the parent function. y= \(2^{x}\) obtain  y=\(2^{x}\)-5.

The focal points are located at a distance of 6.244 units from the center along the major axis in both directions. Therefore, the maximum focal point is (3 - 6.244, 5) ≈ (-3.244, 5), and the minimum focal point is (3 + 6.244, 5) ≈ (9.244, 5).

The given equation of the ellipse is in the standard form: ((x - h)^2)/a^2 + ((y - k)^2)/b^2 = 1, where (h, k) represents the center of the ellipse, and a and b are the semi-major and semi-minor axes, respectively.

From the equation ((x - 3)^2)/225 + ((y - 5)^2)/236 = 1, we can see that a^2 = 225 and b^2 = 236.

The center of the ellipse is located at the point (3, 5).

The end points of the major axis can be found by adding or subtracting the square root of a^2 (which is 15) from the x-coordinate of the center. So, the end points of the major axis are (3 - 15, 5) and (3 + 15, 5), which simplify to (-12, 5) and (18, 5).

Similarly, the end points of the minor axis can be found by adding or subtracting the square root of b^2 (which is approximately 15.36) from the y-coordinate of the center. So, the end points of the minor axis are (3, 5 - 15.36) and (3, 5 + 15.36), which simplify to (3, -10.36) and (3, 20.36).

The focal points of the ellipse can be determined based on the distance from the center. The distance from the center to the focal point along the major axis is given by c = √(a^2 - b^2), where c is the distance from the center to the focal point. Substituting the values, we get c = √(225 - 236) ≈ 6.244. The focal points are located at a distance of 6.244 units from the center along the major axis in both directions. Therefore, the maximum focal point is (3 - 6.244, 5) ≈ (-3.244, 5), and the minimum focal point is (3 + 6.244, 5) ≈ (9.244, 5).

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An equation that matches the table include the following: y = x + 5.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (6 - 5)/(1 - 0)

Slope (m) = 1/1

Slope (m) = 1.

At data point (0, 5) and a slope of 1/, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = 1(x - 0)

y - 5 = x

y = x + 5

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Answer:

Step-by-step explanation:

Therefore , the solution to the given problem of variable is "Is there a substantial association between bullying and depression?".

A variable is a value that can be altered depending on the mathematical issue. Numerous mathematical expressions use the generic letters x, y, and z. Or to put it another way, a variable and equations  is a symbol denoting a number whose value is unknown. Say that x +5 = 10. A variable is used here, "x."

Here,

To see if bullying and depression are significantly related.

Explained: To determine whether there is a meaningful link between the independent and dependent variables, simple linear regression analysis is utilized.

So the approach presented here is the most effective way to answer the research question, "Is there a substantial association between bullying and depression?".

Therefore , the solution to the given problem is "Is there a substantial association between bullying and depression?".

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Answer:

9. y=6x+4

10. y=-1/3x-2

11. y= 2/3x

12. y=-3/2x+2

13. y=2/3x+4/3

14. y=1/2x-3

Step-by-step explanation:

For 9-10, the slope is always x, the y-intercept is the numbers at the end.

11-12: See how much it takes to move up, and then right. That'll be the fraction. Up 2, right 3.

13-14= Graphing cal. from Desmos.

The simplified form of the given function f(g(x)) as required to be determined in the task content is; f (g(x)) = 3x² -24x + 50.

It follows from the task content that the expression which represents f (g(x)) as required in the task content is to be determined.

Given; f(x) = 3x^2+2 and g(x) = x - 4.

Therefore; f (g(x)) = 3 (x - 4)² + 2

= 3 (x² - 8x + 16) + 2

= 3x² - 24x + 48 + 2

f (g(x)) = 3x² -24x + 50.

Ultimately, the expression which represents the function f (g(x)) as required is; f (g(x)) = 3x² -24x + 50.

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Answer: 40.82

Step-by-step explanation:

To calculate the circumference of a circle, multiply the diameter of the circle with π (pi).

13 * 3.14 = 40.82

This may be wrong, but I found this on the internet

a) There are 36 sample points that are possible.

b) The probability of obtaining a value of 7 is 1/12.

c) The probability of obtaining a value of 8 or greater is 1/6.

(a) When rolling a pair of dice, each die has six possible outcomes: 1, 2, 3, 4, 5, or 6. The possible outcomes for the pair of dice can be represented by the set of all ordered pairs (a, b), where a and b represent the outcomes of the first and second die, respectively.

Since each die has six possible outcomes, there are a total of 6 x 6 = 36 possible outcomes for rolling a pair of dice.

(b) To obtain a sum of 7, we must have one die showing 1 and the other die showing 6, or one die showing 2 and the other die showing 5, or one die showing 3 and the other die showing 4, for a total of three possible outcomes.

Since each die has six possible outcomes, there are a total of 6 x 6 = 36 possible outcomes. Therefore, the probability of obtaining a sum of 7 is 3/36, or 1/12.

(c) We must have one die showing 2 and the other die showing 6, or one die showing 3 and the other die showing 5, or one die showing 4 and the other die showing 4, or one die showing 4 and the other die showing 5, or one die showing 5 and the other die showing 3, or one die showing 6 and the other die showing 2, for a total of 5 + 1 = 6 possible outcomes.

Therefore, the probability of obtaining a sum of 8 or greater is 6/36, or 1/6.

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Answer:

Yes.

Step-by-step explanation:

Because

6*4 =24

and 4*0 = 0,

24+0=24

have a nice day!!!

To determine the three angles in a triangle, we can use the Law of Cosines or the Law of Sines. However, since we are not given any side lengths, we will use the dot product formula to find the angles between the sides.

Then, we can compute the magnitudes of these vectors using the Pythagorean theorem:

|AB| = sqrt((Bx - Ax)^2 + (By - Ay)^2)
|AC| = sqrt((Cx - Ax)^2 + (Cy - Ay)^2)
|BC| = sqrt((Cx - Bx)^2 + (Cy - By)^2)

where (Ax, Ay), (Bx, By), and (Cx, Cy) are the coordinates of points A, B, and C, respectively.

Finally, we can use the dot product formula above to compute the cosines of angles A, B, and C, and then take the inverse cosine to find the angles in radians:

A = acos((AB · AC) / (|AB| · |AC|))
B = acos((AB · BC) / (|AB| · |BC|))
C = acos((AC · BC) / (|AC| · |BC|))

where acos denotes the inverse cosine function.

Therefore, we can determine all three angles in the triangle (in radians) using the above formulae.
It seems that the three points of the triangle were not provided in your question. To help you determine the angles of the triangle, please provide the coordinates of the three points (A, B, and C).

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A used book store also started selling used CDs and videos. In the first week, the store sold 40 used CDs  then 30 CDs and 10 Videos were sold.

Given that a used book store also started selling used CDs and videos. In the first week, the store sold 40 used CDs and videos, at 4.00 per CD and 6.00 per video.

The sales for both CDs and videos totaled to 180.00.

Let CDs be x and Videos be y

Then we have x+y =3040

and 4x+6y = 180

Two simultaneous equations in two variables and can be solved by elimination method

multiply I equation by 4 and subtract from II.

2y = 20

y =10

x = 30

30 CDs and 10 Videos were sold.

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Answer:

the answer is -1/3

Step-by-step explanation:

Answer:

400

Step-by-step explanation:

375 , 400, 410 (arrange in asc or des)

median = (middle num) = 400

Hope its right!

Answer:

400

Step-by-step explanation:

Considering the expression of a line, the slope of the line that passes through the points (2,4) and (9,12) is 8/7.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope of the line is calculated as:

m= (y₂ - y₁)÷ (x₂ - x₁)

In this case, being (x₁, y₁)= (2,4) and (x₂, y₂)= (9,12), the slope m can be calculated as:

m= (12 -4)÷ (9 -2)

Solving:

m= 8÷ 7= 8/7

Finally, the slope of the line is 8/7.

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The measure of the arc TQ is 180°.

Given that a circle with an angle subtended outside is 38° and a small arc of 104°, we need to determine the measure of arc TQ.

So, according to the property of a circle, we have,

m ∠R = 1/2 [m arc TQ - m arc SQ]

38° × 2 = m arc TQ - 104°

76° = m arc TQ - 104°

m arc TQ = 76° + 104°

m arc TQ = 180°

Hence the measure of the arc TQ is 180°.

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A moderately intense, wide peak in the 3200-3400 cm⁻¹ region is indicative of the presence of hydroxyl (-OH) functional groups.

Identification of Hydroxyl Functional Groups Using Infrared Spectroscopy

One specific region of the infrared spectrum that can provide valuable information is the 3200-3400 cm⁻¹ region. If an unknown compound displays a moderately intense, wide peak in this region, it is highly likely that it contains a hydroxyl (-OH) functional group.

Infrared spectroscopy is a powerful tool in the identification of functional groups in unknown compounds.

The presence of hydroxyl groups can be further confirmed by looking for other characteristic peaks in the IR spectrum, such as a broad peak in the 1600-1700 cm⁻¹ region for the bending vibrations of the -OH bond. Overall, infrared spectroscopy can be an effective method for identifying hydroxyl functional groups in unknown compounds.

Infrared spectroscopy is a powerful tool in the identification of functional groups in unknown compounds.  This is because the stretching vibration of the -OH bond falls in the range of 3200-3400 cm⁻¹ and the hydroxyl group is characterized by a broad, intense peak due to the high density of vibrational modes.

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The function which represents the cost to drive a car from this agency miles x a day is :

C(x) = 15, if 0 ≤ x ≤ 200

      = 15 + 0.05x, if x > 200

Given that,

A car rental agency charges $15 a day for driving a car 200 miles or less.

The function can be written as,

C(x) = 15 if 0 ≤ x ≤ 200

If a car is driven over 200 miles, the renter must pay $0.05 for each mile over 200 driven.

C(x) = 15 + 0.05x, if x > 200

Hence the correct option is D.

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Answer:.

1.43%

2100/300=7

So they bought each shirt for 7 dollars.

Now they are selling them at 10 dollars.

OK so, now we will divide 10 by 7 which is: 1.42857143

and once you simplify its 1.43%

Step-by-step explanation:

my instagram account bdq.frk follow please

Answer:

Step-by-step explanation:

Formula

Geometric Mean = √(x1*x2)^(1/2)

This is the formula for 2 numbers. You multiply the two givens together and take the square root of the 2 numbers multiplied together. If there were 3 numbers, you would take the cube root.

Givens

x1 = 7

x2 = 20 Put the givens in the formula

Solution

Geometric mean = (7 * 20)^(1/2)

Geometric Mean = (140)^(1/2)

Geometric Mean = 11.83  Rounded.

Answer:

Below

Step-by-step explanation:

Find the lenght of ONE round    3520 / 4 = 880 ft

Circumference of a circle = pi * d

                                 880 ft = pi * d

                                    880 ft / pi = d = 280.11 =~ 280 ft

Answer:

an = 6 * 2^(n-1)

Step-by-step explanation:

To find the general term of the sequence 6, 12, 24, 48, ... , we need to observe that each term is obtained by multiplying the previous term by 2. Therefore, the sequence is a geometric sequence with first term a = 6 and common ratio r = 2.

The formula for the nth term of a geometric sequence is:

an = a * r^(n-1)

Substituting a = 6 and r = 2, we get:

an = 6 * 2^(n-1)

Therefore, the general term of the sequence 6, 12, 24, 48, ... is given by the formula an = 6 * 2^(n-1).

Calculating this expression will give us the amount the farmer needs to save annually over the 8-year period.

Given:

Payment required at the end of each year: P50,000

Number of years until the daughter starts college: 8

Interest rate: 7% (compounded annually)

We can calculate the annual savings using the formula for the present value of an ordinary annuity:

P = \dfrac{PMT \times (1 - (1 + r)^{-n}{r}

Where:

P = Present value (amount to be saved annually)

PMT = Payment amount (P50,000)

r = Interest rate per period (7% or 0.07)

n = Number of periods (8)

Let's substitute the given values into the formula:

\[ P = \dfrac{50,000 \times (1 - (1 + 0.07)^{-8}{0.07} \]

Calculating this expression will give us the amount the farmer needs to save annually over the 8-year period.

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