A 30
-foot-tall street lamp casts a 16.5
-foot-long shadow. Use the reciprocal functions and the Pythagorean Theorem, as necessary, to determine the distance from the top of the lamppost to the farthest part of the shadow. What is the angle at which the street lamp casts its shadow?

Answer:

155.5 square feet

Step-by-step explanation:

A = (1/2)(10)(8.6 + 6.3 + 8.6 + 7.6)

= 5(31.1)

= 155.5 square feet

The fraction equivalent to 3/8 with a numerator and denominator product of 216 is 9/24.

To find the fraction equivalent to 3/8 with a numerator and denominator product of 216, follow these steps:

Set up an equation for the product of the numerator and denominator:

x × y = 216.

Since the fraction is equivalent to 3/8, you can write another equation: x / y = 3/8.

Solve for x in terms of y in the second equation:

x = (3/8) × y.

Substitute this expression for x in the first equation:

(3/8) × y × y = 216.

Solve for y: [tex]y^2 = (8/3) × 216.[/tex]

Simplify the equation: y^2 = 576.

Find the square root of both sides: y = 24.

Now, find x using the equation x = (3/8) × y:

x = (3/8) × 24.

Simplify the expression:

x = 9.

So, the fraction equivalent to 3/8 with a numerator and denominator product of 216 is 9/24.

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It would take the faster computer 525/20 minutes to do the job on its own.

Let the rate of the faster computer be F and the rate of the slower computer be S. Since they can complete the job together in 15 minutes, we have:

F + S = 1/15

We also know that the slower computer takes 35 minutes to do the job on its own, so:

S = 1/35

Now, we can substitute the value of S into the first equation to solve for F:

F + 1/35 = 1/15

F = 1/15 - 1/35

F = (35 - 15) / (15 * 35)

F = 20 / 525

Therefore, the rate of the faster computer is 20/525. To find how long it takes the faster computer to do the job on its own, we take the reciprocal of this rate:

Time = 1/F = 525/20

So, it would take the faster computer 525/20 minutes to do the job on its own.

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The first five terms are 2, 6, 18, 54, 162.

A number is a fundamental building block of mathematics.

Numbers are used for indexing, counting, measuring, and a variety of other tasks.

According to their characteristics, there are various sorts of numbers, including natural numbers, whole numbers, rational and irrational numbers, integers, real numbers, complex numbers, even and odd numbers, etc.

The resultant number can be calculated by using the fundamental arithmetic operations for integers.

Tally marks were formerly used before numbers.

Numbers are a crucial aspect of our daily lives, from the number of rounds we run around the race track to the number of hours we sleep at night, and much more.

According to our question-

a series where each subsequent term is obtained by multiplying the preceding one by a shared ratio.

The order is provided by:

a, ar, ar2, aar3, aar4, aar5,...

What is the nth term provided by-

a_n = ar^(n-1)

Second term = 6

a_2 = ar^(2-1)

6 = ar^1

6 = ar

Hence, The first five terms are 2, 6, 18, 54, 162.

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the first five terms of the geometric sequence can be either [tex]{2, 6, 18, 54, 162} or {-2, 6, -18, 54, -162}.[/tex]

Assume that "a" is the first letter of the geometric sequence and "r" is the common ratio.

According to the problem statement, the second term is 6. Therefore, we have:

[tex]ar = 6 .....(1)[/tex]

Similarly, the fourth term is 54, which gives us:

[tex]ar^3 = 54 .....(2)[/tex]

We must first determine the values of "a" and "r" in the geometric sequence. The two equations mentioned above can be solved simultaneously to achieve this.

The result of dividing equation [tex](2)[/tex] by equation [tex](1)[/tex] is

[tex]r^2 = 9[/tex]

When we square the two sides, we obtain:

r = ±3

Now, using equation (1), we can find the value of "a" as follows:

[tex]ar = 6[/tex]

Substituting r = 3, we get:

[tex]3a = 6[/tex]

[tex]a = 2[/tex]

Substituting [tex]r = -3[/tex], we get:

[tex]-3a = 6[/tex]

[tex]a = -2[/tex]

Therefore, the first term of the geometric sequence is either  [tex]2[/tex] or [tex]-2[/tex]  , and the common ratio is 3 or -3.

If the first term is 2 and the common ratio is 3, then the first five terms of the geometric sequence are: [tex]2, 6, 18, 54, 162[/tex]

The first five terms of the geometric sequence are as follows, if the common ratio is three and the first term is two:

[tex]-2, 6, -18, 54, -162[/tex]

So, the first five terms of the geometric sequence can be either [tex]{2, 6, 18, 54, 162} or {-2, 6, -18, 54, -162}.[/tex]

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we don't have enough information to determine the exact lengths of the streamers or the distance from the center of the floor to where the second streamer is attached.

Sure, I'd be happy to help! Based on the information you provided, we know that Belle is hanging two streamers of different lengths at the peak of the ceiling for her brother's surprise birthday party. The center of the floor is directly underneath the ceiling peak.

We also know that the distance along the floor from the center of the room to where the first streamer is attached is 6 feet.

Since the second streamer is attached to the floor further from the center of the floor than the first streamer, we can infer that the second streamer is longer than the first streamer.
I hope this helps! Let me know if you have any other questions.

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As, the scale factor is less than 1 . So, the dilation is the reduction for the image of triangle ABC.

How very much larger (as well as smaller) any item becomes following the transformation is indicated by the dilation factor.

Given data:

A'B'C' is the dilation of triangle ABC.

Scale factor = 1/2  = 0.5

As, the scale factor is less than 1 . So, the dilation is the reduction for the image of triangle ABC

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Answer:

3 and 5

Step-by-step explanation:

|x-4| = 1 is the same as x-4 = 1 and -x+4 = 1

x-4=1

x = 5

-x+4 = 1

-x = -3

x = 3

The experimental probability that the number rolled was even is 53 over 100.

In a die 2, 4 and 6 are even numbers so sum of there frequency are possible outcome.

Frequency of 2 4 and 6 are 20,18 and 15 respectively.

Possible outcome = 20+18+15 = 53

Total outcome is sum of all frequency, total outcome = 17+20+14+18+16+15 = 100

P(even) = 53/100

Therefore the experimental probability that the number rolled was even is 53 over 100.

The probability of an event is a number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1, or, using percentage notation, in the range from 0% to 100%. The more likely it is that the event will occur, the higher its probability.

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If a simple random of size n is drawn from a population, then the 95% confidence-interval about "μ", if the sample size "n" is 23 is (101.68 , 110.32).

The population from which a simple random of size "n" is drawn is normally distributed,

We have to construct "95% confidence-interval" when n = 23,

So, c = 0.95, n = 23,

⇒ degree of freedom(df) = 23 - 1 = 22,

from t-distribution table, the critical-value corresponding to c = 0.95 and df = 22 is t = 2.074,

the lower bound is = x' - (t×s)/√n = 106 - (2.074×10)/√23 = 101.68,

the upper bound is = x' + (t×s)/√n = 106 + (2.074×10)/√23 = 110.32,

Therefore, the required 95% confidence interval is (101.68 , 110.32).

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The given question is incomplete, the complete question is

A simple random of size n is drawn from a population that is normally distributed, the sample mean (x') is found to be 106, and the sample standard deviation is 10. Construct a 95% confidence interval about "μ", if the sample size "n" is 23.

The factorization for 8i is 3x(5x+1)(x-2), which can also be checked by multiplying the factors and verifying that the result is equal to the original polynomial.

Polynomial     GCF Factored with GCF Factored TrinomiaL  Final  

9x^4 + 3x^3 -1222 1     NA                                   NA                                        

2x^2 + 3x - 9        1    NA     (2x-3)(x+3)                    (2x-3)(x+3)

15x^3 - 27x^2 - 6x 3x 3x(5x^2 - 9x - 2) not factorable 3x(5x+1)(x-2)

9a) Factorization from 8d: not factorable

9b) Factorization from 8h: (2x-3)(x+3)

9c) Factorization from 8i: 3x(5x+1)(x-2)

Note: The table shows the factoring process for each polynomial. In question 9, we just need to check the final factorization for each of the polynomials in question 8. The factorization for 8d is not factorable, so there is nothing to check. The factorization for 8h is (2x-3)(x+3), which can be checked by multiplying the factors and verifying that the result is equal to the original polynomial.

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The total number of possible three-digit numbers is not odd, does not contain 6, and has at least one repeated digit is 13,221,888.

To find the number of possible three-digit numbers we need to use the systematic approach method

Step 1:

we have to find the number of three-digit numbers that are not odd. Number of possible choices for the units digit (0, 2, 4, or 8)= 4

Number of possible choices for tens and hundreds of digits (0-9 excluding 6 = 9

the total number of three-digit numbers that are not odd is,

= 4 x 9 x 9

= 324.

Step 2:

Count the number of three-digit numbers that do not contain 6.

Number of possible choices for each digit (0-5, 7, 8, or 9) = 8

the total number of three-digit numbers that do not contain 6 is,

= 8 x 8 x 8

= 512.

Step 3:

Count the number of three-digit numbers that do not have distinct digits. The number of possible choices for the repeated digit and 9 choices for the other digit = 9

the total number of three-digit numbers that have a repeated digit is

= 9 x 9 = 81.

Step 4:

Find the intersection of the sets of numbers counted in Steps 1-3.

To do this, we multiply the number of choices in each set:

= 324 x 512 x 81

= 13,221,888.

Therefore, 13,221,888 possible three-digit numbers are not odd, do not contain 6, and have at least one repeated digit.

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A horizontal compression is identified by a factor inside the function, affecting the input variable, while a vertical compression is identified by a factor outside the function, affecting the output variable.

When examining the formula of a function that is the result of multiple transformations, a horizontal compression can be identified by a factor that appears inside the function, affecting the input variable (typically x). For example, if the original function is f(x) and the horizontal compression is by a factor of 2, the function would be written as f(x/2), indicating that the input values are being compressed horizontally.

On the other hand, vertical compression can be identified by a factor that appears outside the function, affecting the output variable (typically y). For example, if the original function is f(x) and the vertical compression is by a factor of 1/2, the function would be written as (1/2)f(x), indicating that the output values are being compressed vertically.

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The true statement about effect size is: The effect size is the extent to which the null or statistical hypothesis is false. Effect size is a measure used in research studies to quantify the magnitude of the difference between groups or the strength of an association between variables.

It helps determine the practical significance of the research findings, as opposed to the statistical significance.
When the effect size is small, detecting it is not necessarily easier, and a larger sample size may be required to achieve adequate statistical power. A larger effect size, on the other hand, might be easier to detect and might require a smaller sample size.
There is not just one type of effect size measure used in research studies. There are various measures of effect size, such as Cohen's d, Pearson's correlation coefficient (r), and odds ratio (OR), among others. Each type of effect size is suitable for different research designs and data types.

Choosing the appropriate effect size measure depends on the research question, the design of the study, and the type of data being analyzed.

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The perimeter of the rectangle is 38 feet, the predicted perimeter is 26 feet, the area of the rectangle is 30 square feet, and the predicted area is also 30 square feet.

The formulas for the perimeter and area of a rectangle are:

Perimeter = 2(length + width)

Area = length x width

In these formulas, "length" refers to the longer side of the rectangle, and "width" refers to the shorter side of the rectangle. The perimeter is the total length of the sides of the rectangle, and the area is the amount of space inside the rectangle.

To find the perimeter of the rectangle, we simply add up the lengths of all four sides:

Perimeter = 10 feet + 3 feet + 6 feet + 6 feet + 4 feet + 9 feet

Perimeter = 38 feet

To predict the perimeter, we could use the formula for the perimeter of a rectangle, which is:

Predicted Perimeter = 2(length + width)

We can find the length and width of the rectangle by finding the longest and shortest sides:

Length = 10 feet

Width = 3 feet

Therefore, the predicted perimeter would be:

Predicted Perimeter = 2(10 feet + 3 feet)

Predicted Perimeter = 26 feet

To find the area of the rectangle, we multiply the length by the width:

Area = 10 feet × 3 feet

Area = 30 square feet

To predict the area, we could use the formula for the area of a rectangle, which is:

Predicted Area = length × width

Using the same values for length and width as before, the predicted area would be:

Predicted Area = 10 feet × 3 feet

Predicted Area = 30 square feet

Therefore, the perimeter of the rectangle is 38 feet, the predicted perimeter is 26 feet, the area of the rectangle is 30 square feet, and the predicted area is also 30 square feet.

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y=f(x) has vertex (-4,6)

g(x)=-f(x-2) shifts the graph 2 units to the right, not to the left, and the graph is reflected over the x-axis

therefore the vertex is (-2,6) and the reflection over the x-axis has no affect on the vertex

To  draw the image of triangle △ABC under a dilation with center C and scale factor 2, we need to draw the original triangle, draw lines from C to each vertex,

To draw the image of triangle △ABC under a dilation with center C and a scale factor of 2, we need to follow a few steps. Firstly, we need to draw the original triangle △ABC. Then, we need to draw a straight line from the center of dilation C to each vertex of the triangle. These lines will act as our guides for where the new vertices will be located.

Next, we need to use the scale factor of 2 to determine the distance between the original vertices and the new vertices. This means that we need to multiply the distance between each vertex and the center of dilation by 2. We can then plot the new vertices along the lines we drew in the previous step.

Finally, we can connect the new vertices to form the image of the triangle under the dilation. This image will be twice as large as the original triangle and will be located in the same direction as the lines we drew from the center of dilation to each vertex.

use the scale factor to determine the new vertex locations, and finally connect the new vertices to form the image.

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Answer:

0.0399148483 is the answer

Answer:

Your answer is 0.0399

Step-by-step explanation:

The perimeter of a shape is the measurement around its edge and it is 101.36 in.

We must sum up the lengths of the quadrilateral four sides to determine its perimeter. Since there are two of each side measurement, it is easy to accomplish this by simply adding the length and width and multiplying the result by two.

Perimeter of given shape = 18 + 27 +27 + perimeter of the arc

the perimeter of the arc = Perimeter of the semicircle = [tex]\pi r[/tex]

Therefore the perimeter of the shape = 72 + 3.14 * 9 = 101.36 in.

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10t + 4p ≤ 25 inequality shows the maximum number of tables and people Nathaniel can invite while staying within his budget.

What is inequality?

In mathematics, an inequality is a statement that two values or expressions are not equal, but rather that one is greater than or less than the other. An inequality is denoted by the symbols "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).

Let the number of tables Nathaniel buys be represented by t, and the number of people he invites be represented by p.

Then, the total cost can be expressed as:

Cost = 100t + 40p

Since Nathaniel does not want to spend more than 250, we can set up the inequality:

100t + 40p ≤ 250

We can simplify this inequality by dividing both sides by 10:

10t + 4p ≤ 25

This inequality shows the maximum number of tables and people Nathaniel can invite while staying within his budget.

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The area of the kitchen in square feet is 132[tex]ft^{2}[/tex]

To find the area of the rectangular kitchen, we need to multiply the length by the width.

The length of the kitchen can be found by subtracting the x-coordinates of the two points on the same vertical side. So, the length is 8 - (-3) = 11 feet.

The width of the kitchen can be found by subtracting the y-coordinates of the two points on the same horizontal side. So, the width is 4 - (-8) = 12 feet.

Therefore, the area of the kitchen is:

Area = Length x Width = 11 ft x 12 ft = 132 square feet

So the answer is 132[tex]ft^{2}[/tex].

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Answer:

covered distance = 97.75 kilometers

Step-by-step explanation:

It's known that:

[tex]speed = \frac{distance}{time}[/tex]

Hence,

[tex]distance = speed\times time[/tex] (*)

Given That:

time = 4.25 hours
speed = 23 km/h

then, by substituting in (*):

[tex]distance = 23 \times 4.25 = 97.75 kilometers[/tex]


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Option A, For the aptitude puzzle, the number of ways each of people has the same number of internet friends is 60.

We want to count the number of ways that the 6 people can be internet friends with each other given that each person has the same number of internet friends and no one has an internet friend outside of the group.

Let k be the number of internet friends each person has. Since each person knows 5 other people in the group, we have 6k = 5 * 6, which means that k=5.

Thus, each person has 5 internet friends. We can choose these 5 friends in 5 to choose 5 times 4 choose 5 times 3 choose 5 times 2 choose 5 times 1 choose 5 = 1 × 0 × 0 × 0 × 0 = 0 ways since we can't choose 5 friends from fewer than 5 people.

Therefore, the answer is (A) 60.

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The question is -

Adam, Benin, Chiang, Deshawn, Esther, and Fiona have internet accounts. Some, but not all, of them are internet friends with each other, and none of them has an internet friend outside this group. Each of them has the same number of internet friends. In how many different ways can this happen?

a. 60

b. 170

c. 290

d. 320

e. 660

To increase the value of the expression 1/3A-B^2, increasing A and keeping B constant will cause the expression's value to increase.

This is because the expression has a linear term of A and a quadratic term of B^2. Increasing A will result in a larger linear term, which will increase the value of the expression. None of the other options will necessarily increase the value of the expression. Keeping AAAA constant and decreasing BBBB or decreasing A and keeping B constant will both cause the value of the expression to decrease while keeping AAAA constant and increasing BBBB will only increase the quadratic term of the expression and may or may not result in an overall increase depending on the values of A and B.

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3,523 gallons

Answer:

Step-by-step explanation:

im assuming your saying number 3 which is yes

The polygon is translated five units to the right.

A translation does not alter the appearance of a shape; it merely shifts it up, down, or from side to side. A metamorphosis serves as an example of translation. A transformation is a method for changing a shape's size or placement. At each location, the shape is translated in the same direction by the same amount.

The polygon ABCD's vertices are provided to us as A (-1, -1); B (1, -5); C (5, -5) and D (3, -1)

Also, the vertices of second polygon A'B'C'D' are given as A' (4, -1); B' (6, -5); C' (10, -5) and D' (8, -1).

It is evident that neither polygon's y coordinates have changed.

A 5 increment is made to the x-coordinates.

The translation rule in use is therefore (x, y) → (x + 5, y)

As a result, the polygon is translated 5 units to the right.

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The complete question is:

Graph of polygon ABCD with vertices at negative 1 comma negative 1, 1 comma negative 5, 5 comma negative 5, 3 comma negative 1.

A second polygon A' B' C' D' with vertices at 4 comma negative 1, 6 comma negative 5, 10 comma negative 5, 8 comma negative 1.

Determine the translation used to create the image.

1. 5 units to the right

2. 1 unit to the right

3. 5 units to the left

4. 1 unit to the left

The area of a rectangle is 140.00 square meters.

What is a rectangle?

A rectangle is a 2-dimensional geometric shape with four sides, where each interior angle is a right angle (90 degrees). It is a special case of a parallelogram, where opposite sides are equal in length and parallel to each other.

I assume you are looking for the area of a rectangle with sides 10 m and 14 m, rounded to the nearest hundredth using the approximation π ≈ 3.14.

The area of a rectangle is given by the formula A = lw, where l and w are the length and width of the rectangle, respectively. In this case, l = 14 m and w = 10 m, so:

A = lw = (14 m)(10 m) = 140 m²

Rounding 140 to the nearest hundredth gives 140.00, so the final answer is:

140.00 square meters.

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Full question:

What is the area of a rectangle with sides of length 10 meters and 14 meters, rounded to the nearest hundredth using the approximation π ≈ 3.14?

Answer:

20

Step-by-step explanation:

You can find this answer multiple ways.

One way is that each y value increases by 5 so following the pattern of 5, 10, 15 the next one would be 20.

Another way is that the the x value is 3 times the y value so we would just have to divide 60 by 3 to get 20.

Answer: 20

Step-by-step explanation:

y is a result of dividing x by 3

15/3 = 5

30/3 = 10

...

60/3 = 20

Answer:

[tex]3 \: {cm}^{2} [/tex]

Step-by-step explanation:

Given:

h (height) = 1,5 cm

b (base) = 4 cm

Find: A (area) - ?

[tex]a = \frac{1}{2} \times b \times h[/tex]

[tex]a = \frac{1}{2} \times 4 \times 1.5 = 3 \: {cm}^{2} [/tex]