A bridge is to be built across a small lake from a gazebo to a dock (see figure). The bearing from the gazebo to the dock is S 41° W. From a tree x = 90 meters from the gazebo, the bearings to the gazebo and the dock are S 74° E and S 28° E, respectively. Find the distance from the gazebo to the dock. (Round your answer to the nearest whole number.)

[tex]2+b(a^2+4)[/tex] when a is 2 and b is 4

Substitute for variables with given values:

[tex]2+(4)((2)^2+4)[/tex]

[tex]=\fbox{34}[/tex]

Using compound interest formula, the final payment for a principal of $12000 compounded continuously at rate of 5% is $13,097.31

Compound interest is the interest calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan. It is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest.

The formula of compound interest is given as;

A = P(1 + r/n)^nt

Substituting the values into the formula

A = Pe^rt

This formula is only for continuously compounded

A = 12000e^(0.05 * 1.75)

A = $13,097.31

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Answer:

The equation to find the number of fourth-grade students in the group (f) is:

(number of vans) x (number of students per van) + (number of third-grade students) = (number of fourth-grade students)

So, the equation would be:

4v x 8s + 27s = f

Where "v" stands for vans, "s" stands for students, and "f" stands for fourth-grade students.

To find the number of fourth-grade students, you would need to substitute in the given information:

4 x 8 + 27 = f

32 + 27 = f

So, there are 59 fourth-grade students in the group.

Step-by-step explanation:

The container can hold 1.12 pounds

A container can hold a maximum of 17.75 pounds

There are two objects in the container

The first object weights 6.53 pounds

The second object weight 10.1 pounds

The amounts of pounds that the container can hold is

6.53+10.1

= 16.63

17.75-16.63

= 1.12

Hence the container can hold 1.12 pounds

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The function F(x) = 2/x has a removable discontinuity at x = 0, and a non-removable discontinuity at x = 0.

What is the Function?

A function is a mathematical relation between a set of inputs, called the domain, and a set of possible outputs, called the range. The definition of a function is often written as "f: X → Y", where X is the domain and Y is the range, and "f" is the name of the function.

The function F(x) = 2/x has a removable discontinuity at x = 0, and a non-removable discontinuity at x = 0.

At x = 0, the function is not defined, so it has a removable discontinuity at x = 0.

However, since the function is not defined for x = 0, it is also a non-removable discontinuity at x = 0.

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Answer:

Step-by-step explanation:

1. One solution. Solving for g gives g=2.

2. No solution. The equation is equivalent to -3b = -3b, which is always false.

3. One solution. Solving for f gives f=2/5.

4. Infinite solutions. The equation is equivalent to 2n-12 = 2n-12, which is always true for any value of n.

5. Infinite solutions. The equation is equivalent to 7c-4 = 7c+3, which is always true for any value of c.

6. One solution. Solving for y gives y = -3/7.

7. One solution. Solving for w gives w = -22

8. One solution. Solving for h gives h = 2

9. One solution. Solving for j gives j = -2

10. One solution. Solving for u gives u = -5

11. One solution. Solving for a gives a = -1/2

12. No solution. The equation is equivalent to 3-11d = -11d+3, which is always false.

Answer:

The cost per hour for renting the boat is $18 per hour.

A function is said to be linear if it is a straight line graph and it can be represented by the equation:

y = mx + b

where y, x are variables, m is the rate of change and b is the initial value of y.

Let y represent the total cost for renting the boat for x hours.

Given the equation:

y = 18x

Therefore the cost per hour for renting the boat is $18 per hour.

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Answer: Rutendo's mistake was ordering the recipes from least to greatest by bananas per muffin by comparing the number of bananas in each recipe rather than the number of bananas per muffin. ✅

Step-by-step explanation:

By dividing the number of bananas used in each recipe by the number of muffins, he would have been able to determine which recipe uses the least amount of bananas per muffin.

Recipe A: 3/12 = 0.25 bananas per muffin

Recipe B: 5/24 = 0.208 bananas per muffin

Recipe C: 11/48 = 0.229 bananas per muffin

So Recipe A uses the least amount of bananas per muffin, Recipe C uses the next least amount of bananas per muffin, and Recipe B uses the most amount of bananas per muffin.

Answer: The answer is C

Step-by-step explanation:

Because it is

Answer:

x = 60

Step-by-step explanation:

x and 60 are alternate interior angles and since the lines are parallel, x = 60.

x = 60

Answer:

60°

Step-by-step explanation:

We know that, if two line are parallel, alternate angles are equal.

B D // X Y

Therefore,

x = 60°

Step-by-step explanation:

what is so confusing ? let me know, where you need more explanation.

the angle PTS = 96°

that is the angle between the outer left and the outer right line, so the total angle of everything in the graphic.

now we see 2 sub-angles in there :

PTQ = 28°

RTS = 49°

and we are looking for a third sub-angle QTR.

well, we know, all 3 angles together are the same as the one big angle defined at the beginning.

PTS = PTQ + RTS + QTR

96 = 28 + 49 + QTR

96 - 28 - 49 = QTR

QTR = 19°

Answer:

x = 128.57°

y = 51.43°

Step-by-step explanation:

x = (n - 2) × 180°/n = (7 - 2) × 180°/7 = 900/7° = 128.57°

x + y = 180

y = 180° - 128.57°

y = 51.43°

We shall see that a maximum of 8 teams can be created, with 3 boys and 4 girls on each team.

The largest factor that will divide into two or more numbers is known as the highest common factor (HCF). The smallest multiple shared by two or more numbers is known as the lowest common multiple (LCM). A number that divides two or more numbers precisely is referred to as a common factor. For instance, because they are both even, 10 and 20 share a common factor of 2. The largest number that precisely divides two or more numbers is known as the greatest common factor (GCF).

given

32 girls and 24 boys

Additionally, we must divide them into groups in order to determine the number of groups that can be formed. To do this, we must determine the highest common factor between 24 and 32.

To obtain that, we can express both of these as a prime number product as follows:

24 = 2*2*2*3

32 = 2*2*2*2*2

The highest common factor between 24 and 32 is 2*2*2 = 8 since in all of these we have three times the factor 2.

Each squad will have the following number of boys 24/8 = 3

Each team will have four girls, or 32/8, total.

We shall see that a maximum of 8 teams can be created, with 3 boys and 4 girls on each team.

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Because by multiplying by 8/3, you're multiplying by 1/3, 8 times. (8*1/3=8/3)

Regression analysis is mostly used when you want to predict a continuous dependent variable from a several number of independent variables. If the dependent variable is dichotomous, then logistic regression can be used.

If the break between the two levels of the dependent variable is nearly to 50-50%, then we can use both logistic and linear regression will end up giving you similar results.

If you have inserted the data (rather than using an established dataset), it is a nice idea to check the accuracy and the consistence of the data entry.

If you do not want to re-check all the data point, you should at least check the minimum and maximum value for all the variable to ensure that all values for each variable are "valid" or not.

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''Start with a line and point K on that line'' is the next step in constructing a line perpendicular to a segment

Whenever two lines cross at a right angle, they are perpendicular or orthogonal. All four of the angles created by two perpendicular lines are 90 degrees.

If and only if the slope product of two non-vertical lines is negative one, those lines are perpendicular. In other words, two perpendicular lines' slopes are the negative reciprocals of one another. A vertical line is perpendicular to only horizontal lines and has an infinite slope (which have slope 0).

This provides a way to determine if two lines are parallel by using their equations. Additionally, this enables us to discover the equations of lines that are perpendicular to another line.

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There are 1.057 quarts in a liter, and there are 0.946 liters in a quart.

5 Quarts =4.7317647 Liters

5 Liters =5.2834410 Quarts

The cost is In liter calculate

5 qt.: $2.25=4.7317647 liter

5 liters: $2.35=1000×5=5000

=5000-4.731

= 4,995.269 litter difference from 5 liter

5000 liter in liter $2.35 so each value 2,127.65957447

4.731 liter in of quarts $2.25 each value 2,102.66666667

1 qt = 2pt For every quart there are 5 qts = 10 pts two pints. So, multiply 5 x 2 = 10 pints. Example: If a pot has a capacity of 16 cups, how many quarts can it hold? 1 qt = 4c For every quart, there are 4 cups. The quart (symbol: qt) is an English unit of volume equal to a quarter gallon. Three kinds of quarts are currently used: the liquid quart and dry quart of the US customary system and the imperial quart of the British imperial system. All are roughly equal to one liter.

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The closest number of 2 is 63/32. By using the subtraction operation, we can compute it.

What are numbers?

A number is a mathematical object that can be used to count, measure, and name things. The natural numbers 1, 2, 3, 4, and so on are the original examples. Number words can be used to represent numbers in language.

Given numbers are [tex]1\frac{15}{16}[/tex], 17/8, 63/32

Now find the difference between the given numbers from 2.

The difference of   [tex]1\frac{15}{16}[/tex] from 2 is

2 - [tex]1\frac{15}{16}[/tex]

= 2 - 31/16

= 1/16.

The difference of 17/8 from 2 is

|2 - 17/8|

= |(16 - 17)/8|

=| -1/8|

= 1/8

The difference of 63/32 from 2 is

2 - 63/32

= (64 - 63)/32

= 1/32

The numerator of the difference is the same. The greater denominator represents a less number.

Thus 63/32 is close to 2.

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The rule for the transformation that dilates point B(4, -16) by a scale factor of 3 is: (x, y) --> (3x, 3y)

A transformation is a function that maps points in a given space to points in a different space. There are many types of transformations, including translations, rotations, dilations, and reflections.

A coordinate is a set of numerical values that are used to specify the position of a point in a specific space. In two-dimensional space, a point is typically defined by an ordered pair of numbers (x, y), where x is the horizontal position and y is the vertical position. In three-dimensional space, a point is typically defined by an ordered triple of numbers (x, y, z), where x, y, and z are the positions in the three dimensions.

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On solving the provided question, we can say that A dilation is a transformation that yields a different-sized picture with the same general shape as the original.

A dilation in mathematics is a function f from a metric space M to itself that, for any point x, y in M, fulfills the identity d = rd. where r is a positive real integer and d is the separation between x and y. Such extensions are identical in space according to Euclid. Dilation is a transform that modifies an object's size. The process of dilation is used to enlarge or reduce items. The result of this transformation is an image that is a perfect replica of the original shape. However, there is a variation in the shape's size. The initial form ought to be distorted by dilation.

A dilation is a transformation that yields a different-sized picture with the same general shape as the original. The scale factor (also known as the dilation constant) and the dilation center are included in the description of a dilation. A fixed point in the plane around which all points are enlarged or contracted is the center of a dilation.

for example

triangle ABC ≈ triangle A'B'C'

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Step-by-step explanation:

AB is the height of tree

angle is 60 degree

bc is the bottom of tree

(a) Truth Table is attached.

(b) In canonical SOP form, A = ∑ m(3,5,6,7)

(c) Minimal form: A = m1m2 + m0m1 + m0m2

(b) Canonical SOP form: The canonical sum-of-products (sop) form of LPP in matrix notation is as follows: Boost Z = CX (objective function) AX b (restrictions) and X 0 (limitations) apply (non-negativity restrictions).

it will be A = ∑ m(3,5,6,7)

(c) Minimal form: The k-map can be defined as a map that provides a pictorial method of grouping together expressions with common factors and therefore eliminating unwanted variables. The Karnaugh map can also be described as a special arrangement of a truth table.

it will be A = m1m2 + m0m1 + m0m2

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The complete question is:

a museum has three rooms, each with a motion sensor (m0,m1, and m2) that outputs 1 when motion is detected. at night, the only person in the museum is one security guard who walks from room to room. create a circuit that sounds an alarm (by setting an output a to 1) if motion is ever detected in more than one room at a time, meaning there must be at least one intruder.

(a) Specify the truth table

(b) formulate canonical sum of products implementation for A

(c) Minimize A using K-maps and write the minimum implementation of A

According to the Angle Addition Postulate, the measure of m∠ABD = 202°.

According to the Angle Addition Postulate, an angle's measure is equal to the sum of the measures of any two adjacent angles. The Angle Addition Postulate can be used to determine the measurement of a missing angle or to determine the angle produced by two or more other angles.

Given:

The angle measures:

m∠ABC=37°,

and m∠⁡C⁣B⁣D= 165⁢°.

So, according to the angle addition postulate;

m∠ABD = m∠ABC + m∠CBD

Substituting the values,

m∠ABD = 37° + 165⁢°

m∠ABD = 202°

Therefore, the angle measure of m∠ABD = 202°.

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If we want to find the volume of the given toy, then the units of our answer will be (A) cm³.

Volume is the amount of space a thing takes up, whereas capacity is the amount of solid, liquid, or gas that it can hold.

Volume is measured in cubic units, although capacity can be expressed in almost any other unit, such as liters, gallons, pounds, etc.

The capacity of an object is measured by its volume.

For instance, a cup's capacity is stated to be 100 ml if it can hold 100 ml of water in its brim.

The quantity of space occupied by a three-dimensional object can also be used to describe volume.

So, in the description, it is stated that the value is measured in cubic units.

Therefore, if we want to find the volume of the given toy, then the units of our answer will be (A) cm³.

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The last boxplot is the one that displays the values range  of the distribution that is given.

The range of a function in mathematics can refer to one of two ideas that are connected in some way: Codomain for the function an illustration of the action If there is precisely one y in Y and there are two sets X and Y, then a binary relation f between X and Y is a function that connects x and y.

Here ,Given information:

6,7,9,9,20,22,26,28,29,30

N = 10 observations were made.

The base number is 6. ( least value)

Quartile lower= n+1(0.25)

term = 0.25(13) = 3.25term = 13

Median equals 0.5 (n + 1)

term = 0.5(13) = 6.5 term = (20 + 24) /2 = 22

Upper quartile: 0.75 (13)

A term equals 9.75 a term equals 26.5

Interquartile Range (IQR) is equal to= Q3 - Q1= (26.5 - 13) = 13.5

The highest value is 30. (highest value in the distribution)

As a result, the Last boxplot is the one that shows the distribution that is given.

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Answer:

x = -4

Step-by-step explanation:

3x + 5= -7

bring the 5 to the other side

3x = -12

divide both sides by 3

x = -4

Answer:

[tex] \sf \: x = - 4[/tex]

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ 3x + 5 = -7

Then the value of x will be,

→ 3x + 5 = -7

→ 3x = -7 - 5

→ 3x = -(7 + 5)

→ 3x = -12

→ x = -12 ÷ 3

→ [ x = -4 ]

Hence, the value of x is -4.

Answer:

what your question tell me I will give you answer and also write down your name and question

A horizontal x-axis and a vertical y-axis make up the line graph.

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Answer:

16 57/60 mins

Step-by-step explanation:

9 1/4 = 555 secs

3 4/5 = 228 secs

30.mins = 1800 secs

time for C = 1800 - 555 - 228

= 1017 sec

16 57/60 mins

Answer:

Multiply price of each burrito by 100

Step-by-step explanation: