A 25-foot tree casts a 10-foot shadow. At the same time, a nearby cell tower casts a 30 -foot shadow. How tall (in feet) is the cell tower?

Answer:

Triangle????????????????? ¿

The angle C in the triangle is 34.05 degrees.

The sum of angles in a triangle is 180 degrees. The angle in a triangle can be found using cosine law as follows:

Therefore, let's find the unknown angle in the triangle as follows;

c² = a² + b² - 2ab cos C

Hence,

4² = 5² + 7² - 2 × 7 × 5 cos X

16 = 25 + 49 - 70 cos X

16 = 74 - 70 cos X

16  - 74 = -70 cos X

-58 = -70 cos X

cos X = 58 / 70

X = cos⁻¹ 0.82857142857

X = 34.0478785629

X = 34.05 degrees

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Answer:

7/4

Step-by-step explanation:

You can think of slope as rise over run, or the change in y / the change in x.

In the image, we can view the two points that are marked on the coordinate system.

We can see how many spaces up we need to go and how many spaces to the right we need to go to find the slope. We can count that we go 7 spaces up and 4 spaces to the right giving us a slope of 7/4. We can also do the change in y over the change in x.

Change in Y: 3 - (-4) = 7

Change in X: (-1) - (-5) = 4

Slope: = Change in Y / Change in X = 7/4

Mercury will travel approximately 10800 miles in 6 minutes.

To convert the speed of Mercury from miles per second to miles per minute, we need to multiply the given speed by the number of seconds in a minute, which is 60.

Speed of Mercury in miles per minute = 30 miles/second [tex]\times[/tex] 60 seconds/minute = 1800 miles/minute

Therefore, Mercury travels at a speed of 1800 miles per minute.

To calculate the distance Mercury will travel in 6 minutes at this speed, we can multiply the speed by the time.

Distance traveled by Mercury in 6 minutes = Speed [tex]\times[/tex] Time = 1800 miles/minute [tex]\times[/tex] 6 minutes = 10800 miles

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a. The probability of spending less than 10 minutes is approximately 0.6255.

b. The probability of spending longer than 5 minutes is 0.9741.

c. The probability of spending between 8 and 15 minutes is 0.7181.

(a) We'll use the z-score formula:

z = (x - μ) / σ

Plugging in the values:

z = (10 - 9.3) / 2.2 ≈ 0.3182

Now, we'll look up the cumulative probability corresponding to the z-score of 0.3182 in the standard normal distribution table or use a calculator. The cumulative probability is approximately 0.6255.

(b) To find the probability of spending longer than 5 minutes, we'll again use the z-score formula:

z = (x - μ) / σ

z = (5 - 9.3) / 2.2 ≈ -1.9545

Therefore, the probability of spending longer than 5 minutes is approximately 1 - 0.0259

= 0.9741.

(c) For 8 minutes:

z1 = (8 - 9.3) / 2.2 ≈ -0.5909

For 15 minutes:

z2 = (15 - 9.3) / 2.2 ≈ 2.5909

Next, we find the cumulative probabilities for these z-scores using a standard normal distribution table or a calculator. The cumulative probability for z1 ≈ 0.2776, and for z2 ≈ 0.9957.

Finally, we subtract the cumulative probability for 8 minutes from the cumulative probability for 15 minutes to get the probability between these two values:

0.9957 - 0.2776

≈ 0.7181

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The expression that What formula(s) below represents the frequency of

that E are Option A, C and E.

A stored expression that can be invoked from other expressions is known as an expression rule. You can use rule inputs in your expression rules to allow you to dynamically alter the data your expression returns.

A finite combination of symbols that are well-formed in accordance with context-dependent principles is called an expression or a mathematical expression.

From the option A, we have [tex]440. 2^{\frac{7}{12} } \\\\[/tex]

Then  this can be written as ; [tex]440 ^{\sqrt[12]{2} }[/tex]

which can be written as [tex]440 .10597^7}[/tex]

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Answer:

6

Step-by-step explanation:

After 300 trials, the experimental probabilities may not align perfectly with the theoretical probabilities. However, with more trials, the experimental probabilities tend to converge towards the theoretical probabilities for closer alignment.

To examine whether experimental probabilities after 300 trials align closely with theoretical probabilities, let's consider an example of flipping a fair coin.

Theoretical probability: When flipping a fair coin, the theoretical probability of obtaining heads or tails is 0.5 each. This assumes that the coin is unbiased and has an equal chance of landing on either side.

Experimental probability: After conducting 300 trials of flipping the coin, we record the outcomes and calculate the experimental probabilities. Let's assume that heads occurred 160 times and tails occurred 140 times.

Experimental probability of heads: 160/300 = 0.5333

Experimental probability of tails: 140/300 = 0.4667

Comparing the experimental probabilities to the theoretical probabilities, we can observe that the experimental probability of heads is slightly higher than the theoretical probability, while the experimental probability of tails is slightly lower.

In this particular example, the experimental probabilities after 300 trials do not align perfectly with the theoretical probabilities. However, it is important to note that these differences can be attributed to sampling variability, as the experimental outcomes are subject to random fluctuations.

To draw a more definitive conclusion about the alignment between experimental and theoretical probabilities, a larger number of trials would need to be conducted. As the number of trials increases, the experimental probabilities tend to converge towards the theoretical probabilities, providing a closer alignment between the two.

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The question probable may be:

Do experimental probabilities after 300 trials tend to align closely with theoretical probabilities? Consider an example scenario and calculate both the theoretical and experimental probabilities to determine if they are close.

The area of the figure WXYZ which can be calculated as the sum of the area of the composite triangles ΔXYZ and ΔXWZ is 12 square units

Composite figures are figures comprising of two or more regular figures.

The slope of the side WZ = 2/5

The slope of YZ = -2/1 = -2

The slope of WZ is not the negative inverse of the slope of YZ, therefore, the figure WZ is not perpendicular to YZ and the figure is not a rectangle.

Considering the two triangles formed by the diagonal XZ, we get;

The figure XYZW is a quadrilateral, which is a composite figure comprising of two triangles, triangle ΔXYZ and ΔXWZ

Area of triangle ΔXYZ = (1/2) × 6 × 2 = 6 square units

Area of triangle ΔXWZ = (1/2) × 6 × 2 = 6 square units

The area of the figure = Area of triangle ΔXYZ + Area of triangle ΔXWZ

Area of triangle ΔXYZ + Area of triangle ΔXWZ = 6 + 6 = 12 square units

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Answer:

[tex]9\frac{1}{2} cm^2[/tex]

Step-by-step explanation:

The area of the shaded region = area of triangle - area of the rectangle

Base, b of the triangle = 3 + 4 = 7 cm

Ar of triangle = base*height/2

= 7*5/2

= 35/2

[tex]=17\frac{1}{2} cm^2[/tex]

ar of rectangle = length *breadth

= 4*2

= 8 cm²

The area of the shaded region = area of triangle - area of the rectangle

[tex]=17\frac{1}{2} - 8\\\\=9\frac{1}{2} cm^2[/tex]

Answer:

16.5 cm²

Step-by-step explanation:

The shaded area is the area of the triangle minus the area of the rectangle.

A = bh/2 - LW

For the triangle,

b = 3 cm + 4 cm = 7 cm

h = 2 cm + 5 cm = 7 cm

For the rectangle,

L = 4 cm

W = 2 cm

A = bh/2 - LW

A = (7 cm)(7 cm)/2 - (4 cm)(2 cm)

A = 24.5 cm² - 8 cm²

A = 16.5 cm²

Answer:

answer is 42

Step-by-step explanation:

use the distance formula and it's simple afterwards. I am pretty sure the answer is correct but let me know if you need more help

Answer:

-13/60

Step-by-step explanation:

trust me

Answer:

You have selected the correct answer.

Step-by-step explanation:

y = mx + b

the slope is the m or the change in y over the change in x.

b is the y value at (0,b)  In this case (0,3).

Answer:

61 hours

Explanation:

In this question we will use radioactive decay model

m0= 250 mg

h is the hlf life of element

m(t) is the mass left after t time

so,solving this equation for h

re aranging and taking ln on both the sides we get

solving further we get

h= 60.62 hours ≅61 hour

the half life of element is 61 hours

Step-by-step explanation:

"The exponential function grows faster than the quadratic function over only one interval" best describes the growth rates of the functions.

A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero.

There are three commonly-used forms of quadratics:

Standard Form: y = a x 2 + b x + c y= [tex]ax^2+bx+c y=ax2+bx+c.[/tex]

Factored Form: y = a ( x − r 1 ) ( x − r 2 ) y= a(x-r_1)(x-r_2) y=a(x−r1)(x−r2)

Vertex Form: y = a ( x − h ) 2 + k y= [tex]a(x-h)^2+k y=a(x−h)2+k.[/tex]

Quadratic functions can be represented symbolically by the equation, y(x) = ax2 + bx + c, where a, b, and c are constants, and a ≠ 0. This form is referred to as standard form.

The statement "The exponential function grows faster than the quadratic function over only one interval" best describes the growth rates of the functions.

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The third term (a3) of the sequence is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183. These values are obtained by applying the given formula recursively and substituting the previous terms accordingly. The calculations follow a specific pattern and are derived using the provided formula.

The sequence is defined by the following formula:

a1 = 1, a2 = 3,

and

an = (-1)nan - 1 + an - 2 for n ≥ 3.

To find the third term (a3), we substitute n = 3 into the formula:

a3 = (-1)(3)(a3 - 1) + a3 - 2.

Next, we simplify the equation:

a3 = -3(a2) + a1.

Since we know a1 = 1 and a2 = 3, we substitute these values into the equation:

a3 = -3(3) + 1.

Simplifying further:

a3 = -9 + 1.

Therefore, the third term (a3) is equal to -8.

To find the fourth term (a4), we substitute n = 4 into the formula:

a4 = (-1)(4)(a4 - 1) + a4 - 2.

Simplifying the equation:

a4 = -4(a3) + a2.

Since we know a2 = 3 and a3 = -8, we substitute these values into the equation:

a4 = -4(-8) + 3.

Simplifying further:

a4 = 32 + 3.

Therefore, the fourth term (a4) is equal to 35.

To find the fifth term (a5), we substitute n = 5 into the formula:

a5 = (-1)(5)(a5 - 1) + a5 - 2.

Simplifying the equation:

a5 = -5(a4) + a3.

Since we know a4 = 35 and a3 = -8, we substitute these values into the equation:

a5 = -5(35) + (-8).

Simplifying further:

a5 = -175 - 8.

Therefore, the fifth term (a5) is equal to -183.

In summary, the third term (a3) is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183.

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The statements that are true about the system of equations are: Options C, D, and E.

Let's analyze each statement and determine whether it is true or false for the given systems of equations:

System A

2x - 3y = 4

4x - y = 18

System B

3x - 4y = 5

y = 5x + 3

System C

2x - 3y = 4

12x - 3y = 54

A. All three systems have different solutions.

To determine if the systems have different solutions, we need to solve them. Solving system A gives the solution x = 5 and y = -6. Solving system B gives the solution x = -1 and y = -2. Solving system C gives the solution x = 5 and y = -6. Therefore, this statement is false because systems A and C have the same solution.

B. Systems B and C have the same solution.

As mentioned above, solving system B gives the solution x = -1 and y = -2. Solving system C gives the solution x = 5 and y = -6. Therefore, this statement is false because systems B and C have different solutions.

C. System C simplifies to 2x-3y=4 and 4x-y=18 by dividing the second equation by three.

To simplify system C, we can divide the second equation by 3, resulting in:

2x - 3y = 4

4x - y = 18

This is exactly the same as system A. Therefore, this statement is true.

D. Systems A and B have different solutions.

As mentioned earlier, solving system A gives the solution x = 5 and y = -6. Solving system B gives the solution x = -1 and y = -2. Therefore, this statement is true.

E. Systems A and C have the same solution.

As mentioned earlier, solving system A gives the solution x = 5 and y = -6. Solving system C gives the solution x = 5 and y = -6. Therefore, this statement is true.

In summary:

A. False

B. False

C. True

D. True

E. True

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Complete Question:

Select all the statements that are true for the following systems of equations.

System A

2x - 3y = 4

4x - y = 18

System B

3x - 4y = 5

y = 5x +3

System C

2x - 3y = 4

12x - 3y = 54

A. All three systems have different solutions.

B. Systems B and C have the same solution.

C. System C simplifies to 2x-3y=4 and 4x-y=18 by dividing the second equation by three.

D. Systems A and B have different solutions.

E. Systems A and C have the same solution.

The bearing from the phone to the transmitter is approximately 31 degrees to the east of the north direction.

To determine the bearing from the phone to the transmitter, we can use trigonometry.

The bearing is typically measured clockwise from the north direction.

Given that the transmitter is 13 km west and 21 km south of the phone, we can form a right triangle with the phone as the vertex angle.

The side opposite to the vertex angle represents the north-south direction, and the side adjacent to the vertex angle represents the east-west direction.

Using the tangent function, we can calculate the angle:

tangent(angle) = (opposite side) / (adjacent side)

tangent(angle) = 21 km / 13 km

Taking the inverse tangent (arctan) of both sides, we find:

angle = arctan(21 km / 13 km)

Evaluating this using a calculator, we find the angle to be approximately 58.57 degrees.

However, since the bearing is measured clockwise from the north, we need to subtract this angle from 90 degrees (which represents the north direction) to obtain the bearing:

bearing = 90 degrees - 58.57 degrees

Calculating this, we find the bearing to be approximately 31.43 degrees.

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Jabez is correct without calculating the product of 54 x 0.06 correctly because his estimation aligns with the mathematical principle that multiplying a number by a decimal less than 1 will result in a smaller product.

To determine who is correct without calculating the product of 54 x 0.06, we can use estimation.
Jabez estimated that the answer will be less than 54 but greater than 5.4. Let's analyze his estimation. When multiplying a number by a decimal less than 1, the product will always be smaller than the original number. In this case, 54 is the original number. Since 0.06 is less than 1, the product of 54 x 0.06 will definitely be smaller than 54.
On the other hand, Christina thinks the answer will be less than 5.4. Let's analyze her estimation. The original number, 54, is already greater than 5.4. When multiplying it by a decimal less than 1, the product will be even smaller. Therefore, Jabez's estimation is incorrect.
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Answer:

(-3, -2) ∪ (1, ∞)

Step-by-step explanation:

Given inequality:

[tex]\dfrac{x^2+5x+6}{x-1} > 0[/tex]

Begin by factoring the denominator:

[tex]\begin{aligned}x^2+5x+6&=x^2+2x+3x+6\\&=x(x+2)+3(x+2)\\&=(x+3)(x+2)\end{aligned}[/tex]

Therefore, the factored inequality is:

[tex]\dfrac{(x+3)(x+2)}{x-1} > 0[/tex]

Determine the critical points - these are the points where the rational expression will be zero or undefined.

The rational expression will be zero when the numerator is zero:

[tex](x+3)(x+2)=0 \implies x=-3,\;x=-2[/tex]

Therefore, -3 and -2 are critical points.

The rational expression will be undefined when the denominator is zero:

[tex]x-1=0 \implies x=1[/tex]

Therefore, 1 is a critical point.

So the critical points are -3, -2 and 1.

Create a sign chart, using open dots at each critical point (the inequality is greater than, so the interval doesn't include the values).

Choose a test value for each region, including one to the left of all the critical values and one to the right of all the critical values.

Chosen test values: -4, -2.5, 0, 2

For each test value, determine if the function is positive or negative:

[tex]x=-4 \implies \dfrac{(-4+3)(-4+2)}{-4-1} = \dfrac{(-)(-)}{(-)}=\dfrac{(+)}{(-)}=-[/tex]

[tex]x=-2.5 \implies \dfrac{(-2.5+3)(-2.5+2)}{-2.5-1} = \dfrac{(+)(-)}{(-)}=\dfrac{(-)}{(-)}=+[/tex]

[tex]x=0 \implies \dfrac{(0+3)(0+2)}{0-1} = \dfrac{(+)(+)}{(-)}=\dfrac{(+)}{(-)}=-[/tex]

[tex]x=2 \implies \dfrac{(2+3)(2+2)}{2-1} = \dfrac{(+)(+)}{(+)}=\dfrac{(+)}{(+)}=+[/tex]

Record the results on the sign chart for each region (see attached).

As we need to find the values for which the rational expression is greater than zero, shade the positive regions on the sign chart (see attached). These regions are the solution set.

Remember that the intervals of the solution set should not include the critical points, as the critical points of the numerator make the expression zero, and the critical point of the denominator makes the expression undefined. The intervals of the solution set are those where the rational expression is greater than zero only.

Therefore, the solution set is:

-3 < x < -2  or  x > 1

As interval notation:

(-3, -2) ∪ (1, ∞)

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The statement that describes the transformations applied in the figure above include the following: C. 7 units left and a reflection about the x-axis.

In Mathematics and Geometry, a reflection over or across the x-axis is represented by this transformation rule (x, y) → (x, -y).

Based on the graph, the coordinates of point A are located at (-6, 1) in quadrant II.

By applying a translation to the A horizontally right by 7 units, the new coordinate A1 of quadrilateral ABCD include the following:

(x, y)                               →                  (x + 7, y)

A (-6, 1)                        →                  (-6 + 7, 1) = A1 (1, 1)

By applying a reflection over the x-axis to the coordinates of point A1, we have the following coordinates of the image A';

(x, y)                              →      (x, -y)

Point A1 (1, 1)             →      A' (1, -(1)) = G' (1, -1)

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The values of the angles given are: 0,90,180,240,270,360,420,480,540,600,630,660,720 and

he sine of an angle is the trigonometric ratio of the opposite side to the hypotenuse of a right triangle containing that angle.  It is defined as the length of the opposite side divided by the length of the hypotenuse

The given angles are: 0,30,45,90,120,135,180,210,225,240,270,300,315,330,360

2∅  2*∅ = 0, 90,180,240,270,360,420,480,540,600,630,660,720

sin 2∅ = sin0 = 0; Sin90=1;  sin180=0; sin240= -0.8660; sin270 = -1;

Each angle is multiplied by sine sine360 =1; sin420 = 0.8660; sin480= 0.9848; sin540=1; sin600=-0.8660; sin630=-1; sin660=0.8660; sin720= 0.9397

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Based on unit conversions, the number of customers that would seat at each table is 12 persons.

The number of customers per table can be determined using unit conversions, which involve multiplication and division.

In this situation, the total available space per table is converted to squared inches from squared feet, and divided by the required table space per customer.

Conversely, the required table space per customer can be converted to squared feet and the result used to divide the total available space per table.

The required table space per customer = 300 in²

The total available space (area) per table = 300 ft²

1 foot = 12 inches

300 ft² = 3,600 in² (12 x 300)

The number of customers per table = 12 (3,600 ÷ 300)

OR:

300 in² = 25 ft² (300 ÷ 12)

The number of customers per table = 12 (300 ÷ 25)

Thus, using unit conversions, we expect the restaurant owner to seat 12 customers per table.

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The area occupied by each table is 300 ft².

Answer:

C

Step-by-step explanation:

just look at point A and the difference to A'.

A was moved 2 units to the left and 4 units up to get A'.

and the same happened, of course, to all other points of the triangle.

so, C is correct.

Answer:

The vertex of the function is at (–3,–16)

The graph is increasing on the interval x > –3

The graph is positive only on the intervals where x < –7 and where

x > 1.

Step-by-step explanation:

The graph of [tex]f(x)=(x-1)(x+7)[/tex] has clear zeroes at [tex]x=1[/tex] and [tex]x=-7[/tex], showing that [tex]f(x) > 0[/tex] when [tex]x < -7[/tex] and [tex]x > 1[/tex]. To determine where the vertex is, we can complete the square:

[tex]f(x)=(x-1)(x+7)\\y=x^2+6x-7\\y+16=x^2+6x-7+16\\y+16=x^2+6x+9\\y+16=(x+3)^2\\y=(x+3)^2-16[/tex]

So, we can see the vertex is (-3,-16), meaning that where [tex]x > -3[/tex], the function will be increasing on that interval

Answer: ∠16 and ∠11

Step-by-step explanation:

      All of these answer options include ∠16, so we know we're looking for an angle that is corresponding to ∠16. A corresponding angle is an angle that is in the same relative position. We will look at ∠9, ∠11, ∠2, and ∠12 since those are the given answer options, and see which is corresponding.

The correct corresponding angles are ∠16 and ∠11.

The approximate mean of the number of cars sold by the salesman in the past 10 weeks is 4.1.

To find the approximate mean, first, we add all the numbers in the data set, and then we divide that sum by the total number of values in the data set.

The formula for finding the approximate mean is as follows: Approximate mean = sum of the values in the data set / total number of values in the data set.

The following data set is given: Number of cars sold by a salesman in the past 10 weeks: 3, 5, 2, 4, 7, 5, 6, 3, 2, 4.

To find the approximate mean, we first need to add all the values: 3 + 5 + 2 + 4 + 7 + 5 + 6 + 3 + 2 + 4 = 41 The sum of all the values is 41.

Next, we need to divide this sum by the total number of values in the data set. In this case, the total number of values is 10. Therefore, the approximate mean for the given data set is: Approximate mean = 41 / 10 = 4.1

Therefore, the approximate mean of the number of cars sold by the salesman in the past 10 weeks is 4.1.

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The best description of the graph is "a quadratic function with a constant difference of 2."

A quadratic function is a function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants. In a quadratic function, the graph forms a parabola.

In the given graph, if the differences between consecutive points on the graph are constant and equal to 2, it indicates a constant difference in the y-values (vertical direction) as the x-values (horizontal direction) increase. This is a characteristic of a quadratic function.

On the other hand, an exponential function with a growth factor of 2 would result in a graph that increases at an increasing rate, where the y-values grow exponentially as the x-values increase. This is not observed in the given graph.

Therefore, based on the information provided, the graph best represents a quadratic function with a constant difference of 2.

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The calculation of a p-value generally requires knowing the statistical test used and the degrees of freedom involved, as well as the direction of the test (one-sided or two-sided). This question doesn't specify which statistical test was used or whether the test was one- or two-sided.

One potential scenario is that a chi-square goodness-of-fit test was used, which is common for comparing observed frequencies with expected frequencies. If this is the case, the observed test statistic value of 7.9527 represents the chi-square statistic. The degrees of freedom would be the number of categories minus 1, which is 5-1 = 4 in this case.

To find the p-value, we would look up the chi-square statistic of 7.9527 in a chi-square distribution table with 4 degrees of freedom or use software that can calculate it.

This question doesn't provide enough information to calculate the exact p-value and normally this would be done using a statistical software package or an online chi-square calculator. However, a typical rule of thumb is that a chi-square statistic greater than about 10 with 4 degrees of freedom would suggest a statistically significant result at the 0.05 level, so it's likely that the p-value here is greater than 0.05 (i.e., the result is not statistically significant at the 0.05 level).

Please note this is an approximation and the actual p-value should be calculated using appropriate statistical software or a chi-square calculator.