a boat heading out to sea starts out at Point A, at a horizontal distance of 1083 feet from the lighthouse/the shore. From that point, the boat's crew measures the angle of elevation to the lighthouse's beacon-light from theat point to be 8 degrees. At some later time, the crew measures the angle of elevation from point B to be 4 degrees. Find the distance from point A to point B. Round your answer to the nearest foot if necessary.

Nam needs to pay VND 63,000 for the two toys after receiving the 10% discount.

Nam asked his mother for permission to buy toys as a gift for Tuan's friend on his birthday.

He chose two toys with list prices of VND 45,000 and VND 25,000, respectively.

However, the good news is that he was able to receive a 10% discount on the total cost of both toys.
To calculate the amount that Nam has to pay for both toys, we first need to calculate the total cost of the two toys.

The cost of the first toy is VND 45,000 and the cost of the second toy is VND 25,000, so the total cost of both toys is:
Total cost = VND 45,000 + VND 25,000 = VND 70,000
Now that we have calculated the total cost of both toys, we can calculate the amount of discount that Nam will receive. The discount is equal to 10% of the total cost, which is:
Discount = 10% x VND 70,000 = VND 7,000
Therefore, the amount that Nam has to pay for both toys after the discount is:
Amount to pay = Total cost - Discount

= VND 70,000 - VND 7,000

= VND 63,000
In conclusion, Nam has to pay VND 63,000 to buy both toys after receiving a 10% discount.

It's a great deal, and Tuan's friend will surely love the toys as his birthday gift.

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The jug used by older adults has a volume of 300 ml. To convert 3 liters to milliliters.

We multiply three by 1000, giving us 3000 ml. The ratio of the jug to the kettle can be simplified to 1:10.

To convert 360°F to °C, we use the formula (360-32) ÷ 1.8, which gives us 182°C rounded off to the nearest 10°C.

The matrix after the operation is:

[tex]\left[\begin{array}{ccc}1&8/3&67/3\\-5&-13&-109\end{array}\right][/tex]

We have,

Matrix

[tex]\left[\begin{array}{ccc}3&8&67\\-5&-13&-109\end{array}\right][/tex]

To get a 1 in row 1.

We apply the operation:

Row 1 ÷ 3

So,

[tex]\left[\begin{array}{ccc}1&8/3&67/3\\-5&-13&-109\end{array}\right][/tex]

Thus,

The matrix after the operation is:

[tex]\left[\begin{array}{ccc}1&8/3&67/3\\-5&-13&-109\end{array}\right][/tex]

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The equation of the circle given at the end of the image is:

(x - 2)² + y² = 16.

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle.

The center of the circle given at the end of the image has the coordinates given as follows:

(2,0).

The center is at (2,0), while one x-intercept of the circumference is at x = 6, that is, point (6,0), hence the radius is given as follows:

r = 6 - 2

r = 4.

Thus the equation of the circle is given as follows:

(x - 2)² + y² = 16.

The circle is given by the image presented at the end of the answer.

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Answer: Since there is no amount of texts given we will have to replace it with a variable, and 0.48 as the co-efficient. So the equation will be 0.48x+3, this is as far as you can get.

Step-by-step explanation:

To compute the monthly sales forecast using a 4-month moving average with the given weights, we can follow these steps:

1. Determine the weights for each of the four months. Based on the provided weights (25%, 20%, 15%, 12%), we can assign the following weights to the respective months in reverse order:

Month 1: 12%

Month 2: 15%

Month 3: 20%

Month 4: 25%

2. Calculate the forecast for each month by multiplying the demand for the corresponding month by the assigned weight and summing them up.

For Month 5:

Forecast = (Demand for Month 5 * Weight for Month 1) + (Demand for Month 4 * Weight for Month 2) + (Demand for Month 3 * Weight for Month 3) + (Demand for Month 2 * Weight for Month 4)

Forecast = (41 * 0.12) + (40 * 0.15) + (33 * 0.20) + (29 * 0.25)

Forecast = 4.92 + 6 + 6.6 + 7.25

Forecast ≈ 24.77

Similarly, you can calculate the forecasts for the remaining months using the same approach.

Month 6:

Forecast = (43 * 0.12) + (41 * 0.15) + (40 * 0.20) + (33 * 0.25)

Month 7:

Forecast = (49 * 0.12) + (43 * 0.15) + (41 * 0.20) + (40 * 0.25)

Month 8:

Forecast = (52 * 0.12) + (49 * 0.15) + (43 * 0.20) + (41 * 0.25)

By performing these calculations, you can determine the monthly sales forecasts for each of the remaining months based on the given demand and weights.

Using this fact, we can find the measure of arc MN. Since angle MSN has a measure of 129 degrees, arc MN must have a measure of 2*129 = 258 degrees.



. Let's call the point where the circle intersects with the line that passes through the center point M.

We also know that the measure of angle MSN (where N is the point where the circle intersects with the line opposite to M) is 129 degrees.

Now, there are a few things we can deduce from this information. First of all, we know that angle MSN is an inscribed angle, since it intercepts an arc of the circle.

We also know that the measure of an inscribed angle is equal to half the measure of the intercepted arc.

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Answer:

  (x, y, z) = (-1, -1, 0)

Step-by-step explanation:

You want the solution to the system of equations ...

The calculator solution is shown in the attachment.

  (x, y, z) = (-1, -1, 0)

The coefficient of the y-variable is 2 or -2, which means we can eliminate y terms by adding pairs of equations. Adding the first equation to each of the other two reduces the system to ...

Adding these two equations together gives ...

  -14z = 0   ⇒   z = 0

Substituting this into the second of the reduced equations gives ...

  9x = -9   ⇒   x = -1

And substituting for x and z in the first of the original equations gives ...

  -3(-1) +2y = 1

  2y = -2 . . . . . . . . subtract 3

  y = -1

The solution is (x, y, z) = (-1, -1, 0).

#95141404393

1) The mean of the number of children is ≈ 1.5

2) the median is 1

3) the 5 number summary is

4) See the box plot attached.

A) Mean = sum of all the children reported by the adults/ number of adults

(0 × 5) + (1 × 3) + (2 × 4) + (3 × 2) + (4 × 0) + (5 × 1) = 22

number of adults
5 + 3 + 4 + 2 + 0 + 1 = 15

Mean = 22/15 ≈ 1.5

B)  to find the median we must arrange all the number in ascending order

0, 0, 0, 0, 0, 1, 1, 1, 2,  2, 2, 2, 3,  3, 5

Thus, 1 is the median when we select the number in the middle.

C) the 5 number summary is

D) See the box plot attached.

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Peter invested $138 in the 12% account and $288 in the 13% account.

Let x be the amount invested in the 12% account and y be the amount invested in the 13% account.

We know that the total amount invested is the sum of the two accounts, so: x + y = total amount invested

We also know that Peter has $150 more in the 13% account, so:

y = x + 150

The total interest earned is $54, which can be expressed as:

0.12x + 0.13y = 54

Substituting y with x + 150, we get:

0.12x + 0.13(x + 150) = 54

Simplifying and solving for x, we get:

0.12x + 0.13x + 19.5 = 54

0.25x = 34.5

x = 138

Therefore, Peter invested $138 in the 12% account and $288 in the 13% account.

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The equation of the parabola that opens down, has vertex (-8,5) and a focal diameter of 28.

To determine the equation of the parabola that opens down, has vertex (-8,5) and a focal diameter of 28, we need to use the standard form of the equation of a parabola:
(x - h)^2 = -4p(y - k)
where (h,k) is the vertex and p is the distance from the vertex to the focus (which is half the focal diameter in this case).
Using the given information, we can plug in the values for h, k, and p:
(h,k) = (-8,5)
p = 28/2 = 14
(x + 8)^2 = -4(14)(y - 5)
Simplifying this equation, we get:
(x + 8)^2 = -56(y - 5)
And that is the equation of the parabola that opens down, has vertex (-8,5) and a focal diameter of 28.

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To obtain 15 gallons of 24% alcohol, you would need to mix 14 gallons of 25% alcohol and 1 gallon of 10% alcohol.

To determine the amounts of 25% alcohol and 10% alcohol needed to obtain 15 gallons of 24% alcohol, we can set up an equation based on the principle of the mixture:

Let x represent the number of gallons of 25% alcohol.

Let y represent the number of gallons of 10% alcohol.

The equation can be set up as follows:

0.25x + 0.10y = 0.24  (15)

0.25x + 0.10y = 3.6

To solve this equation, we need another equation. Since we know that the total volume of the mixture is 15 gallons, we can add a second equation:

x + y = 15

Now we have a system of equations:

0.25x + 0.10y = 3.6

x + y = 15

Now, solving

x = 15 - y

Substituting this value of x into the first equation:

0.25(15 - y) + 0.10y = 3.6

3.75 - 0.25y + 0.10y = 3.6

-0.15y = -0.15

y = 1

and, x + 1 = 15

x = 14

Therefore, to obtain 15 gallons of 24% alcohol, you would need to mix 14 gallons of 25% alcohol and 1 gallon of 10% alcohol.

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The equation help us to get the response to the statements as follows

1. False

2. False

3. True

4. False

The statement is true when the solution of the equation is true with the statement

The given equation is

f(x) = 32 / ( 1 + e⁰°⁵ˣ)

first statement

For x = 3, f(3) = 5.84

For x = 6, f(6) = 1.52

5.82 - 1.52 ≠ 9 ft

False

second statement

For x = 0, f(0) = 16

False

third statement

For x = 1, f(1) = 12.08

this shows a decline hence this is True

fourth statement

The trees maximum height, captured should be 16 ft as it started declining

False

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Applying the Triangle Midsegment Theorem, the length of CD in the triangle is: 44 cm.

Based on the Triangle Midsegment Theorem, the line segment that joins the midpoints of two sides of a triangle is parallel to the third side of the triangle and is also half of the length of the third side.

Thus, BE is the midsegment of the triangle with length of 22 cm. Since CD is the third side of the triangle, therefore we have:

Length of BE = 1/2(length of CD)

Plug in the values:

22 = 1/2(CD)

2 * 22 = CD

44 = CD

Length of CD = 44 cm.

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Answer:

14.0

Step-by-step explanation:

Using sine rule

sin A/a = sin B/b

sin 70/15 = sin 61/b

b sin 70 = 15 sin 61

b = (15 sin 61) / sin 70

b = 13.96126278

b = 14.0

The scale factor here is 2.1.

To calculate the scale factor, you need two corresponding measurements from two similar objects or figures. The scale factor is the ratio of the corresponding lengths or dimensions between the two objects.

Now, the scale factor is

= 12.5 / 5

= 125/50

= 21/10

= 2.1 : 1

Thus, the scale factor here is 2.1.

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Looking at these angles, we can see that they are alternate interior angles. Alternate interior angles are congruent. This means that to solve we will simply need to set the given expressions equal to each other and solve for x.

4x - 23 = 3x + 18

x - 23 = 18

x = 41

Answer: x = 41

Hope this helps!

There are [tex]4[/tex] students in total who went down the slide during recess after counting the sequence.

To determine the total number of students who went down the slide during recess, we need to count the number of times the slide was used and consider that each use represents one student. By analyzing the given data, we can count the occurrences of the letter 'X' in the provided sequence:

[tex]\[ x \quad x \quad xx \quad xx \quad x \quad x \quad xx \quad xx \quad xx \quad xx \quad 0 \quad 1 \quad X \quad XXX \quad xx45 \quad xxxxx \quad X \][/tex]

Counting the 'X's, we find that there are [tex]4[/tex] occurrences. Since each 'X' represents one student going down the slide, the total number of students is [tex]4[/tex].

Therefore, there are [tex]4[/tex] students in total who went down the slide during recess.

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The mean score to the nearest whole number is equal to 5.0

In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:

Mean = [F(x)]/n

For the total number of data based on the frequency, we have;

Total score, F(x) = 1(3) + 2(1) + 3(4) + 4(10) + 5(15) + 6(9) + 7(3) + 8(5)

Total score, F(x) = 3 + 2 + 12 + 40 + 75 + 54 + 21 + 40

Total score, F(x) = 247

Now, we can calculate the mean score as follows;

Mean = 247/50

Mean = 4.94 ≈ 5.0.

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Answer:

46√3

Sorry, it's a lot of steps to elaborate on.

hmm well, let's firstly convert all the mixed fractions to improper fractions, then we'll get the dot product.

[tex]\left < 3\frac{1}{2}~~,~~4\frac{2}{3} \right > \hspace{5em}\left < 7\frac{1}{4}~~,~-8\frac{1}{2} \right > \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}}~\hfill \stackrel{mixed}{4\frac{2}{3}} \implies \cfrac{4\cdot 3+2}{3} \implies \stackrel{improper}{\cfrac{14}{3}} \\\\\\ \stackrel{mixed}{7\frac{1}{4}}\implies \cfrac{7\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{29}{4}}~\hfill \stackrel{mixed}{8\frac{1}{2}} \implies \cfrac{8\cdot 2+1}{2} \implies \stackrel{improper}{\cfrac{17}{2}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\left < 3\frac{1}{2}~~,~~4\frac{2}{3} \right > ~~\cdot~~\left < 7\frac{1}{4}~~,~-8\frac{1}{2} \right > \\\\[-0.35em] ~\dotfill\\\\ \left( \cfrac{29}{4} \right)\left( \cfrac{7}{2} \right)~~ + ~~\left( -\cfrac{17}{2} \right)\left( \cfrac{14}{3} \right)\implies \cfrac{203}{8}-\cfrac{119}{3}\implies \cfrac{-343}{24} ~~ \approx ~~ \stackrel{ \textit{dot product} }{-14.29}[/tex]

Answer:

4√10

Step-by-step explanation:

distance = √((16-4)²+ (12-8)²)

= √(144 + 16)

=√160

=√(4X4X10)

=√4 X √4 X √10

= 2 X 2 X √10

= 4√10

Answer: (0, 5)

Step-by-step explanation:

       To find the y-intercept, we will substitute 0 for x into the equation given. This means we will find (0, y), which is the y-intercept.

Given:

       f(x) = x² + 3x + 5

Substiute:

       f(0) = (0)² + 3(0) + 5

Multiply:

       f(0) = 5

       Based on this, the y-intercept is (0, 5). We can also see this when we graph the function. See attached.

This function relationship is linear because it increases at a constant rate

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = 10.5x

where the slope of the line is m = 10.5

So , function relationship is linear because it increases at a constant rate

Hence , the function is f ( x ) = 10.5x is linear

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Answer:

Step-by-step explanation:

41 + 85 + 180 - x = 180

x = 126

Answer:

Step-by-step explanation:

To avoid dividing by zero, denominator cannot equal 0:

                   [tex]x^2-9\neq 0[/tex]

       [tex](x+3)(x-3)\neq0[/tex]

        [tex]x\neq-3 \text{ and }x\neq3[/tex]

Solution: We cannot use [tex]x=-3 \text{ and }x=3[/tex].

The concentration of the drug after 8 hours is equal to 24 mg/L.

The interval over which the concentration increases is 0 < t < 2.

The interval over which the concentration decreases is 2 < t < ∞.

The drug is at its maximum concentration when t = 2 hours and the maximum concentration is 64 mg/L.

After the drug reaches its maximum concentration, the number of hours that are required for the concentration to decrease to 16 mg/L is 8 hours.

After 1 week and 1 month, we can predict that the concentration of the drug kept decreasing after reaching 20 hours.

For any given function, y = f(x), if the output value (range or y-value) is decreasing when the input value is increased, then, the function is generally referred to as a decreasing function.

By critically observing the graph of the given function, we can reasonably infer and logically deduce the following:

The function is increasing over the interval [0, 2] or 0 < t < 2.

The function is decreasing over the interval [2, ∞] or 2 < t < ∞.

In conclusion, the vertex (2, 64) of the graph represent the point where the drug is at its maximum concentration, which is time (t) = 2 hours and the maximum concentration is y = 64 mg/L.

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Answer:

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

The general equation for conditional probability is:

Using this equation and the given values, we can calculate P(A | B) as follows:

Therefore, P(A | B) = 2/3.

a. The interest that would accrue at Bank A is $1484.32.

b. Kathy would owe $5984.32 at Bank A.

c. The interest that would accrue at Bank B is $201.82.

d. Kathy would owe $4776.82 at Bank B.

e. Kathy would save $1213.03 by using Bank B.

a. The annual interest at Bank A is 21.99%. The simple interest for 18 months can be calculated as:

I = Prt = 4500 x 0.2199 x (18/12) = $1484.32.

Therefore, the interest that would accrue at Bank A is $1484.32.

b. The total amount that Kathy would owe at Bank A is the sum of the principal and interest:

Total = Principal + Interest = $4500 + $1484.32. = $5984.32.

Therefore, Kathy would owe $5984.32 at Bank A.

c. The annual interest rate at Bank B is 2.99%, but there is also a one-time service fee of $75. The interest for 18 months can be calculated as:

I = Prt = 4500 x 0.0299 x (18/12) = $201.82.

Therefore, the interest that would accrue at Bank B is $201.82.

d. The total amount that Kathy would owe at Bank B is the sum of the principal, interest, and service fee:

Total = Principal + Interest + Service fee = $4500 + $201.82 + $75 = $4776.82

Therefore, Kathy would owe $4776.82 at Bank B.

e. By using Bank B, Kathy would save the difference between the total amount owed at Bank A and the total amount owed at Bank B:

Savings = Total at Bank A - Total at Bank B = $5989.85 - $4776.82 = $1213.03.

Therefore, Kathy would save $1213.03 by using Bank B.

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