Bilquis is trying to find the height of a radio antenna on the roof of a local building. She stands at a horizontal distance of 29 meters from the building. The angle of elevation from her eyes to the roof (point A) is 17°, and the angle of elevation from her eyes to the top of the antenna (point B) is 31º. If her eyes are 1. 51 meters from the ground, find the heigh[of the antenna (the distance from point A to point B). Round your answer to the nearest meter if necessary. ​

Answer:

8.19 units.

Step-by-step explanation:

I didn't use desmos, i completed the question with all steps and working and didn't require desmos. Hope this Helps. Question was solved using trignometric ratios.

The number of 6-card hands  in which at least one card from each suit is equal to 8,184,220.

Total number of 6-card hands that can be formed from a deck of 60 cards is,

Using combination formula,

C(60, 6) = 50,063,860

Now, subtract the number of 6-card hands that do not contain at least one card from each suit.

There are 5 ways to choose the suit that will be missing from the hand.

Once this suit is chosen, there are 48 cards remaining in the other suits.

Choose 6 cards from this set, so the number of 6-card hands that do not contain any cards from the chosen suit is,

C(48, 6) = 12,271,512

Overcounted the number of hands that are missing more than one suit.

There are C(5, 2) ways to choose 2 suits that will be missing from the hand.

Once these suits are chosen, there are 36 cards remaining in the other 3 suits.

Choose 6 cards from this set, so the number of 6-card hands that do not contain any cards from the chosen suits is,

C(36, 6) = 1,947,792

We cannot have a 6-card hand that is missing more than 2 suits.

3 suits with no cards in the hand, which is not allowed.

Number of 6-card hands that have at least one card from each suit is,

C(60, 6) - 5×C(48, 6) + C(5, 2)×C(36, 6)

=50,063,860 - 5×  12,271,512 + 10 × 1,947,792

= 50,063,860 -61,357,560 + 19,477,920

= 8,184,220

Therefore, there are 8,184,220 of 6-card hands that have at least one card from each suit.

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A deposit of $2000 earning 4.2% simple interest for 3 years will have a balance of $2252. The estimated balance rounded to the nearest whole number is $2252.

To calculate the balance in the account after 3 years, we can use the formula

balance = principal x (1 + interest rate x time)

Plugging in the values, we get

balance = 2000 x (1 + 0.042 x 3)

balance = 2000 x (1 + 0.126)

balance = 2000 x 1.126

balance = 2252

Therefore, the balance in the account after 3 years is $2252.

As for the estimate, since the interest is simple, we can approximate it by multiplying the interest rate by the number of years and adding it to the principal. So, the estimate would be

estimate = principal x (1 + interest rate x time)

estimate = 2000 x (1 + 0.042 x 3)

estimate = 2000 x (1 + 0.126)

estimate = 2000 x 1.126

estimate = 2252

Rounding to the nearest whole number, the estimate is also $2252.

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The angles that belongs to the right angles category are:

KER must be a right angle because it is an angle formed between a tangent (KE) and a radius (AK) at the point of tangency (K). By the Tangent-Secant Theorem, it follows that the measure of the intercepted arc KR is equal to the measure of the angle ∠KER plus 90 degrees. Since KR is a diameter (and therefore a semicircle), its measure is 180 degrees. Therefore, ∠KER + 90 = 180, which implies that ∠KER = 90 degrees.

∠ARE must be a right angle because it is an inscribed angle that intercepts the diameter KR. By the Inscribed Angle Theorem, the measure of an inscribed angle is half the measure of its intercepted arc. Since KR is a diameter, the intercepted arc is the entire circle, which has a measure of 360 degrees. Therefore, ∠ARE = 360/2 = 180 degrees. Moreover, a diameter and a chord that contains the diameter must form a right angle at the point where they meet (in this case, point A). Hence, ∠ARE is a right angle.

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Image transcribed:

The figure below shows a circle with center A, diameter KR, and secants RE and RI. Which of the angles must be right angles? Select all that apply.

Q

E

R

K

D

∠KIR

∠ARD

∠KER

∠ARE

∠ERI

Given the scenerio in the picture about corn, the statement that is true looking at a significance level of 5% is The result is not statistically significant which implies that spraying the corn plants with the new type of fertilizer does increase the growth rate.

Looking at the statement "The result is not statistically significant,"this means that the p-value (probability value) of the test was greater than 0.05. It could have 0.15 oe 0.2.

When a test is greater than 0.05 or 5 % significance level, it shows that the what is happening to the corn (increase in growth rate) could have been as a result of chance alone.

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The cost of the stock, including the broker's fee, is $50,454.30.

The cost of the stock can be found by multiplying the number of shares purchased by the price per share. In this case, the investor purchased 500 shares of Exxon-mobil stock at $98.93 per share, so the cost of the stock can be calculated as follows:

Cost of stock = Number of shares × Price per share

Cost of stock = 500 × $98.93

Cost of stock = $49,465

However, the broker charges 2% of the cost of the stock, which is an additional fee that needs to be added to the total cost. To find the broker's fee, we can simply multiply the cost of the stock by 2%:

Broker's fee = 2% × Cost of stock

Broker's fee = 2% × $49,465

Broker's fee = $989.30

Therefore, the total cost of the stock, including the broker's fee, is:

Total cost of stock = Cost of stock + Broker's fee

Total cost of stock = $49,465 + $989.30

Total cost of stock = $50,454.30

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The surface area of octagonal pyramid with height of 12 and a side length of 4.24 is 281.477 unit²

Height of octagonal pyramid = 12

Side length of octagonal pyramid = 4.14

The surface area of octagonal pyramid is  

SA = 2s²( 1 + √2) + 4sh

Here, s is side length of the octagonal pyramid = 4.14

h is height of the octagonal pyramid = 12

putting the values in the equation we get

SA = 2 × 4.14 ( 1 + √2 ) + 4 × 4.14 × 12

SA = 82.757 + 198.72

SA = 281.477

The surface area of octagonal pyramid is 281.477

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The lateral area of the triangular pyramid is 11.7 sq ft and the total surface area is 15.6 sq ft.

To find the lateral area and total surface area of the triangular pyramid with base and faces as equilateral triangles, we can follow these steps:

1: Find the area of one equilateral triangle.

To find the area of an equilateral triangle with side length 3 ft and height 2.6 ft, we can use the formula:

Area = (1/2) × base × height

Area = (1/2) × 3 × 2.6 = 3.9 sq ft

2: Calculate the lateral area.

Since the pyramid has three equilateral triangles as faces, we can multiply the area of one triangle by 3 to find the lateral area:

Lateral Area = 3 × 3.9 = 11.7 sq ft

3: Calculate the total surface area.

The total surface area includes both the lateral area and the base area. Since the base is also an equilateral triangle with the same dimensions, we can simply add the area of the base to the lateral area to find the total surface area:

Total Surface Area = Lateral Area + Base Area = 11.7 + 3.9 = 15.6 sq ft

In conclusion, the lateral area is 11.7 sq ft and the total surface area is 15.6 sq ft.

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Answer:

k = 1

Step-by-step explanation:

We can use the table for g(x) = f(kx) to find the value of k.

Notice that when x = -2, we have g(-2) = f(k(-2)) = f(-2k) = 64. Similarly, when x = 2, we have g(2) = f(k(2)) = f(2k) = 64.

Using the fact that f(x) is a quadratic function, we can see that its axis of symmetry passes through the vertex at (0, 0), which means that the x-coordinate of the vertex is 0. This tells us that the coefficient of the x term in f(x) is 0, so the function can be written as f(x) = ax^2 + bx + c, where a is not equal to 0.

Using the points (−2,4), (−1,1), (0,0), (1,1), and (2,4), we can write a system of equations to solve for a, b, and c:

a(-2)^2 + b(-2) + c = 4

a(-1)^2 + b(-1) + c = 1

a(0)^2 + b(0) + c = 0

a(1)^2 + b(1) + c = 1

a(2)^2 + b(2) + c = 4

Simplifying and rearranging, we get:

4a - 2b + c = 4

a - b + c = 1

c = 0

a + b + c = 1

4a + 2b + c = 4

Substituting c = 0 into the system, we get:

4a - 2b = 4

a - b = 1

a + b = 1

4a + 2b = 4

Solving this system of equations, we get a = 1, b = -1, and c = 0.

Substituting these values into g(x) = f(kx), we get:

g(x) = f(kx) = x^2 - x

Substituting the values from the table into this equation, we get:

g(-2) = 4 = (-2)^2 - (-2) = 4k

g(2) = 4 = (2)^2 - (2) = 4k

Solving for k, we get k = 1 or k = -1/4.

However, we need to check which value of k satisfies all the points in between -2 and 2, so we can check g(-1) = 1 = (-1)^2 - (-1) = k, and g(1) = 1 = (1)^2 - (1) = k.

Thus, the value of k that satisfies all the points is k = 1, and therefore the answer is:

k = 1

We can use the information given to find the value of k.

Since the vertex of the quadratic function f(x) is at (0,0), we know that the equation for f(x) is in the form of f(x) = ax^2 for some constant a.

Using the point (-2, 4) on the graph of f(x), we can set up the equation 4 = 4a, which gives us a = 1.

So, the equation for f(x) is f(x) = x^2.

Now, we can use the table for g(x) = f(kx) to find the value of k.

When x = -2, we have g(-2) = f(k(-2)) = f(-2k) = 4k^2.

Similarly, when x = 2, we have g(2) = f(k(2)) = f(2k) = 4k^2.

We also know that g(0) = f(k(0)) = f(0) = 0, and g(-1) = f(k(-1)) = f(-k) = k^2 and g(1) = f(k(1)) = f(k) = k^2.

Using the values from the table, we can set up the following system of equations:

4k^2 = 64

k^2 = 16

0 = 0

k^2 = 16

The only solution that works for all of these equations is k = 4 or k = -4.

Therefore, the value of k is either k = 4 or k = -4.

The angle in each quadrant with a common reference angle with 306° are

To find angles in each quadrant with a common reference angle with 306°, we first need to determine the reference angle for 306°.

Reference angle is the acute angle between the terminal side of an angle and the x-axis. We can find the reference angle for any angle θ by subtracting the nearest multiple of 180° from θ and taking the absolute value of the result. In this case:

|306° - 180°| = 126°

So, the reference angle for 306° is 126°.

Now, we can find an angle in each quadrant with a common reference angle of 126°:

1st quadrant: The angle with a reference angle of 126° in the 1st quadrant is simply 126°.

2nd quadrant: To find the angle with a reference angle of 126° in the 2nd quadrant, we need to subtract the reference angle from 180° (since all angles in the 2nd quadrant are between 90° and 180°).

180° - 126° = 54°

So, an angle with a reference angle of 126° in the 2nd quadrant is 54°.

3rd quadrant: To find the angle with a reference angle of 126° in the 3rd quadrant, we need to subtract the reference angle from 180° and then add 180° (since all angles in the 3rd quadrant are between 180° and 270°).

180° + 126° = 306°

So, an angle with a reference angle of 126° in the 3rd quadrant is 306°.

4th quadrant: To find the angle with a reference angle of 126° in the 4th quadrant, we need to subtract the reference angle from 360° (since all angles in the 4th quadrant are between 270° and 360°).

360° - 126° = 234°

So, an angle with a reference angle of 126° in the 4th quadrant is 234°.

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There are 17,576,000 different license plates possible, considering 26 letters (A-Z) and 10 numbers (0-9).

There are 26 options for each of the three letters and 10 options for each of the three numbers. Therefore, using the multiplication principle, the total number of possible license plates is 26 x 26 x 26 x 10 x 10 x 10 = 17,576,000.

Alternatively, we can use the permutation formula to calculate the number of arrangements: P(26,3) x P(10,3) = 15,600 x 720 = 11,251,200.

However, since order does not matter in a license plate, we need to divide by the number of permutations of three letters and three numbers, which is 3! x 3! = 36, resulting in 11,251,200 / 36 = 17,576,000 possible license plates.

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The product of matrices C and D is:

[tex]CD = \left[\begin{array}{ccc}-6&18&-4\\\end{array}\right][/tex]

The best answer is option b.

A matrix (plural matrices) is a set of numbers arranged in rows and columns so as to form a rectangular array.

The number of rows of a matrix can be determined by counting from top to bottom and the number of columns can be determined by counting from left to right.

The product (multiplication) of matrices C and D is:

CD = C * D

[tex]CD = \left[\begin{array}{ccc}2\\9\\4\end{array}\right] * \left[\begin{array}{ccc}-3&2&-1\\\end{array}\right][/tex]

To get the product, multiply each row by the column. That is:

2 * (-3) = -6

9 * 2 = 18

4 * (-1) = -4

[tex]CD = \left[\begin{array}{ccc}-6&18&-4\\\end{array}\right][/tex]

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Ruby and Emma can assemble one gift basket in 0.1818 minutes, together. They will finish the 54th basket at  7:27 PM.

To solve the problem, we first need to find how many gift baskets Ruby and Emma can assemble in one minute.

Ruby can assemble 2/22 = 1/11 gift basket in one minute.

Emma can assemble 4/44 = 1/11 gift basket in one minute.

Together, they can assemble 1/11 + 1/11 = 2/11 = 0.1818 (rounded to four decimal places) gift baskets in one minute.

To assemble the 54th gift basket, they need to assemble 53 gift baskets before that.

53 gift baskets / 0.1818 gift baskets per minute = 291.8181 minutes

Since they start at 1:00 p.m. and Emma starts 15 minutes later, they will finish 291.8181 minutes after 1:15 p.m., which is approximately 7:27 p.m.

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Answer:

Step-by-step explanation: The vertex is the point at the bottom if the parabola opens up and at the top if it opens at the bottom.

The t critical value at 29 degrees of freedom and 0.01 level of significance is 2. 46

Using Critical value calculator we calculate the values.

a) at n = 10

Therefore degrees of freedom is = n - 1= 9, So therefore at 9 degrees of freedom and 0.01 level of significance, t critical value is 2.82

b) at n= 20

Degrees of freedom is 19.

The t critical value at 19 degrees of freedom and 0.01 level of significance is 2.54

c) at n = 30

Degrees of freedom is 29.

So therefore t critical value at 29 degrees of freedom and 0.01 level of significance is 2. 46

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Flo ate more of the sandwich than Arnie.

Option A is the correct answer.

We have,

We need to compare the values 3/4 and 2/3 to determine which fraction represents a larger amount of sandwiches eaten.

To make the fractions comparable, we need to find a common denominator.

The least common multiple of 4 and 3 is 12.

So we can rewrite 3/4 and 2/3 with 12 as the denominator:

3/4 = 9/12

2/3 = 8/12

Comparing these fractions, we see that 9/12 (or 3/4) is greater than 8/12

(or 2/3).

Therefore,

Flo ate more of the sandwich than Arnie.

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Answer:

-12+3(-11)-40-10

Step-by-step explanation:

Answer:

Step-by-step explanation:

-12+12-45-40+1

0-85+1

-84

Using the cosine law, the measure of angle R is calculated as approximately: a. 44.5°.

The cosine law is expressed as follows:

cos R = [s² + q² – r²]/2sq

Given the following side lengths of triangle QRS:

Side q = 11,

Side r = 17,

Side s = 23.

Plug in the values into the cosine law formula:

cos R = [23² + 11² – 17²]/2 * 23 * 11

cos R = 361/506

Cos R = 0.7134

R = cos^(-1)(0.7134)

R ≈ 44.5°

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The sets of side lengths that could form a right triangle are 36-48-60 (option b) and 14-48-50 (option d).

To determine which of these sets of side lengths could form a right triangle, we will use the Pythagorean theorem (a² + b² = c²), where a and b are the shorter sides and c is the hypotenuse. Let's evaluate each option:

a) 4-7-10
Applying the Pythagorean theorem: 4² + 7² = 16 + 49 = 65, which is not equal to 10² (100). So, this set does not form a right triangle.

b) 36-48-60
Applying the Pythagorean theorem: 36² + 48² = 1296 + 2304 = 3600, which is equal to 60² (3600). So, this set does form a right triangle.

c) 6-10-14
Applying the Pythagorean theorem: 6² + 10² = 36 + 100 = 136, which is not equal to 14² (196). So, this set does not form a right triangle.

d) 14-48-50
Applying the Pythagorean theorem: 14² + 48² = 196 + 2304 = 2500, which is equal to 50² (2500). So, this set does form a right triangle.

In conclusion, the sets of side lengths that could form a right triangle are 36-48-60 (option b) and 14-48-50 (option d).

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Answer:  10/12

Step-by-step explanation:

since they give you adjacent to angle m and hypotenuse use

cos x = opp/hyp

cos M = 10/12

For k = 0 and k = 16, there are rational solutions to the quadratic equation [tex]x^{2} + kx + 4k = 0[/tex]

We are given a quadratic equation [tex]x^{2} + kx + 4k = 0[/tex]

An algebraic equation in x with a degree of 2 is known as a quadratic equation. It is written in the format [tex]a[/tex][tex]x^{2}[/tex] [tex]+ bx + c[/tex] = 0. To find out whether there exists two solutions, one solution, or no solution for a quadratic equation, we use the discriminant of the quadratic equation.

We will find the solutions to this quadratic equation with the help of discriminant formula

As we know from the equation that b = k, a = 1, and c = 4k.

[tex]b^2 - 4ac = 0[/tex]

[tex]k^2 - 4(4k) = 0[/tex]

[tex]k^2 - 16k = 0[/tex]

k (k-16) = 0

k = 0    or    k - 16 = 0

k = 0    or    k = 16

So, for k = 0 or k = 16 the equation [tex]x^{2} + kx + 4k = 0[/tex] has only one solution.

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The mean absolute deviation of the given data set is approximately 2.16.

To find the mean absolute deviation (MAD), we first need to calculate the mean of the data set:

Mean = (10 + 10 + 9 + 8 + 10 + 5 + 6 + 4 + 8 + 4) / 10 = 7.4

Next, we calculate the absolute deviation of each data point from the mean:

|10 - 7.4| = 2.6

|10 - 7.4| = 2.6

|9 - 7.4| = 1.6

|8 - 7.4| = 0.6

|10 - 7.4| = 2.6

|5 - 7.4| = 2.4

|6 - 7.4| = 1.4

|4 - 7.4| = 3.4

|8 - 7.4| = 0.6

|4 - 7.4| = 3.4

Then, we find the average of these absolute deviations:

MAD = (2.6 + 2.6 + 1.6 + 0.6 + 2.6 + 2.4 + 1.4 + 3.4 + 0.6 + 3.4) / 10 ≈ 2.16

Therefore, the mean absolute deviation of the given data set is approximately 2.16.

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To find f'(4) for the function f(x) = ln(2x^3), we first need to find the derivative f'(x) using the chain rule.

The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.

For f(x) = ln(2x^3), the outer function is ln(u) and the inner function is u = 2x^3.

The derivative of the outer function, ln(u), is 1/u.
The derivative of the inner function, 2x^3, is 6x^2 (using the power rule).

Now, apply the chain rule: f'(x) = (1/u) * 6x^2 = (1/(2x^3)) * 6x^2.

Simplify f'(x): f'(x) = 6x^2 / (2x^3) = 3/x.

Now, find f'(4): f'(4) = 3/4.

So, f'(4) for f(x) = ln(2x^3) is 3/4 or 0.75 when rounded to 2 decimal places.

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Answer: x = -1, y = 6

Step-by-step explanation:

lets substitute the value of y from the first equation into the y in the second equation.

-2x + 4 = -3x + 3

4 - 3 = -3x + 2x

1 = -1x

x = -1

we know from before that y = -2x + 4

so y = -2(-1) + 4

y = 6

The equation that could represent each of the graphed polynomial function include the following:

First graph: y = x(x + 2)(x - 3)

Second graph: y = x⁴ - 5x² + 4

In Mathematics and Geometry, a polynomial graph simply refers to a type of graph that touches the x-axis at zeros, roots, solutions, x-intercepts, and factors with even multiplicities.

Generally speaking, the zero of a polynomial function simply refers to a point where it crosses or cuts the x-axis of a graph.

By critically observing the graph of the polynomial function shown in the image attached above, we can logically deduce that the first graph has a zero of multiplicity 1 at x = 2 and zero of multiplicity 1 at x = -3.

Similarly, we can logically deduce that the second graph has a zero of multiplicity 2 at x = 2 and zero of multiplicity 2 at x = -2.

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The fourth graph best represents a quadratic function with a range of all real numbers greater than or equal to 3

The graph that best represents a quadratic function with a range of all real numbers greater than or equal to 3 is a graph that opens upward and has a vertex at the point (h, k), where k is the minimum value of the function.

Since the range is all real numbers greater than or equal to 3, the minimum value occurs at or above 3.

Therefore, the vertex of the quadratic function lies on or above the horizontal line y = 3.

Hence, the fourth graph best represents a quadratic function with a range of all real numbers greater than or equal to 3

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With the given pay increase Daniel will earn a total of $185,141.90 in 4 years .

To find out how much Daniel will earn in 4 years with a starting salary of $42,000 and a 6.5% pay increase every year, follow these steps:

1. Calculate the annual salary for each year by applying the percentage increase.
2. Sum up the salaries for all 4 years.

Step 1: Calculate the annual salary for each year
Year 1: $42,000
Year 2: $42,000 * (1 + 6.5%) = $42,000 * 1.065 = $44,730
Year 3: $44,730 * (1 + 6.5%) = $44,730 * 1.065 = $47,656.95
Year 4: $47,656.95 * (1 + 6.5%) = $47,656.95 * 1.065 = $50,754.95

Step 2: Sum up the salaries for all 4 years
Total earnings = $42,000 + $44,730 + $47,656.95 + $50,754.95 = $185,141.90

Daniel will earn a total of $185,141.90 in 4 years with the given pay increase.

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Answer:

6cm

Step-by-step explanation:

all the sides of a square are identical so we can assume the missing side as x

since all four sides are the same and the perimeter is the sum of all sides, we can write

x+x+x+x=24cm

4x=24cm

x=24/4

x=6cm

Answer:

BC= 47.424

I believe that’s correct, but if you really need an answer just get a triangle calculator