Mr. Jakarta is having a well built in his backyard. On Monday 175 feet of the well was drug, and another 165 feet was dug tuesday. How many feet deep was well dug relative to ground level

By applying trigonometric identities, the value of tan(x) = 14, gives;

[tex]sin(2 \cdot x) = \frac{28}{197} [/tex]

[tex]cos(2 \cdot x) = -\frac{195}{197} [/tex]

[tex]tan(2 \cdot x) = -\frac{28}{195} [/tex]

Given;

tan(x) = 14

sin(x) is negative

By definition, we have;

[tex]sin(2 \cdot x) = \mathbf{\frac{2 \cdot \: tan(x)}{1 + {tan(x)}^{2} }} [/tex]

Which gives;

[tex]sin(2 \cdot x) = \frac{2 \times 14}{1 + {14}^{2} } = \frac{28}{197} [/tex]

Similarly, we have;

[tex]cos(2 \cdot x) = \mathbf{\frac{1- tan(x)^2}{1 + {tan(x)}^{2} }} [/tex]

Which gives;

[tex]cos(2 \cdot x) = \frac{1- 14^2}{1 + {14}^{2} } = -\frac{195}{197} [/tex]

[tex]tan(2 \cdot x) = \mathbf{\frac{sin(2 \cdot x) }{cos(2 \cdot x) } } [/tex]

Which gives;

[tex]tan(2 \cdot x) = \frac{ \frac{28}{197}}{-\frac{195}{197} } = -\frac{28}{195} [/tex]

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There are no solutions for z³ = x³ + y³ for a right triangle

The equation is given as:

z³ = x³ + y³

By Pythagoras theorem, we have:

z² = x² + y²

Multiply both sides by z

z³ = zx² + zy²

By comparing z³ = zx² + zy² and z³ = x³ + y³, we have:

x³ + y³ = zx² + zy²

Factor out z

x³ + y³ = z(x² + y²)

Make z the subject

z = (x³ + y³)/(x² + y²)

There exist no solution for the above equation

Hence, there are no solutions for z³ = x³ + y³ for a right triangle

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Answer: B

Step-by-step explanation:

Using the distance formula, we get the height is [tex]4\sqrt{2}[/tex].

Similarly, we get the base is [tex]6\sqrt{2}[/tex].

So, the area is [tex]\frac{1}{2}(4\sqrt{2})(6\sqrt{2})=24[/tex]

The values when the given numbers are multiplied will be:

230

78

3

91

1800

3. 5 × 23 × 2

It should be noted that the given information simply means that we should multiply 5 by 23 by 2. This will be:

= 5 × 23 × 2

= 230

5. 34 + 0 + 18 + 26

This information simply means that we should add thirty four, eighteen, and twenty six together. This will be:

34 + 0 + 18 + 26 = 78

7. (3 × 10 × 8) = ....... × (10 × 8)

(3 × 10 × 8) = 3 × (10 × 8)

9. 0 + ...... = 91

It simply means the number that will be added to zero that will give ninety one. This will be 91.

11. The total income for the theater will be:

= (20 × 18) × 5

= 1800

Therefore, the correct values based on the computation will be 730, 78, 3, 91, and 1800.

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The equilibrium level if autonomous expenditures are $2,000 and the mpe is 0. 5 is $4000.

From the information given, the autonomous expenditures are $2,000 and the mpe is 0. 5.

Here, the equilibrium level will be:

= 2000/(1 - 0.5)

= 2000/0.5

= 4000

In conclusion, the correct option is $4000.

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The height of the basketball hoop to the nearest foot will be 12ft .

There are two ways to continue. The first method is to use trigonometric ratios.

You can use the tangent ratio because you have specified one leg and are trying to solve it with the other leg.

x equals the length of the other leg. .. Plug in known values.

Another way to find out is to monitor the angle. If the two angles are 45 degrees and 90 degrees, you can see that the third angle is 45 degrees. This makes it an isosceles triangle. That is, the other leg is 7 feet long.

2) Determine the height of the tire

Add 7 feet and 5 feet (human height):

7 + 5 = 12 feet

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A ratio is a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

In Mathematics, a fraction comprises two (2) main parts and these include:

3 to 2 = 3/2

5:6 = 5/6

8 to 12 = 3/2

Thus, a common denominator of 12 can be used to rewrite the fractions and then you should compare the numerators to order the ratios in an ascending order.

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Answer:

ABC is congruent to DEF

Step-by-step explanation:

I think its this one cause the angles are the same

Answer:

i need this too hahahaha

The relationship between the natural variation and specifications is quantified by a measure known as the Process capability index.

According to the questions,

The relationship between the natural variation and specifications is quantified by a measure known as the Process capability index.

Process capability index refers to the capability of a process to deliver output which lies within the specifications limits that are desired.

Hence, the relationship between the natural variation and specifications is quantified by a measure known as the Process capability index.

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Using it's formula, the area of the right triangle is of 750 inches squared.

The area of a right triangle is given by half the multiplication of the two legs, which are the two smaller sides.

In this problem, the two legs are 25 inches and 60 inches, hence the area of the triangle is:

A = 0.5 x 25 x 60 = 750 inches².

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If you register a 0. 08 bac or refuse to take a breath test, your license will be automatically suspended for 12 months.

The amount of alcohol in your blood is determined via a blood alcohol(bac)test. The breathalyzer test, which police officers frequently administer to people they suspect of driving while intoxicated, is more widely known. While breathalyzers provide quick findings, they are not as precise as bac tests that measure alcohol in the blood.

The same 0.08 bac limit applies to adults in all 50 states who are 21 years of age or older, who are driving while intoxicated and breaching the law.

No amount of alcohol is safe when you are driving, even if your bac is below the legal limit. Don't drive after drinking, please!

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The total surface area, in m², of the sunshade is 0.4344 m²

A pyramid can have a squared base, rectangular base or other polygons. The formula we can to find the total surface area of a squared pyramid is

Surface Area = P x l/2

Where

Given that a sunshade on one set of equipment has a square base of 120 cm and a height of 50 cm. That means that the length L of the base will be  120 cm and half of it will be 60 cm

To find the slant height l, we will use Pythagoras theorem.

[tex]l^{2}[/tex] = 60² + 50²

[tex]l^{2}[/tex] = 3600 + 2500

[tex]l^{2}[/tex] = 6100

l = √6100

l = 78.1 cm

convert it to meter

l = 78.1/100

l = 0.781 m

The perimeter P of the base = 4 x 120/100 = 4.80 m

The Surface Area = P x l/2

Substitute all the necessary parameters into the formula

Surface Area = 4.80 x 0.781/2  

Surface Area = 1.8744 m²

If the sunshades are open-bottomed square based pyramids, this means that the base is not included. That is, the area of the base should be taken away from the answer above.

Area of the base = 120/100 x 120/100 = 1.44 m²

The total surface area, in m², of the sunshade will 1.8744 - 1.44

The total surface = 0.4344 m²

Therefore, the total surface area, in m², of the sunshade is 0.4344 m²

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Using sampling concepts, it is found that:

a) The best method is: 25 adult residents are randomly selected from the city;

b) The estimate is that 11,536 adults voted in the election.

It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population. A sample has to be representative of the population, that is, it has to involve all segments of the population.

In this problem, the sample will be representative if all adults, no matter if senior or not, homeowners or not are represented, hence the best method is:

25 adult residents are randomly selected from the city;

The estimate of the number of adults that voted is:

14/25 x 20,600 = 11,536.

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Step-by-step explanation:

well there is a very simple point that you have mistaken tho:

484cm², 25cm²

Areas are defined in square cm but the radius is in cm

so:

[tex] \sqrt{ \frac{484 {cm}^{2} }{25 {cm}^{2} } } = \frac{7.92}{r} = = = > 4.4 = \frac{7.92cm}{x} = = > x = \frac{7.92cm}{4.4} = x = 1.8cm[/tex]

and there you go

Answer:

23

Step-by-step explanation:

  In arithmetic sequence, the difference between any consecutive terms is constant and the progression goes either in  ascending order or in descending order.

a = first term = 2

a₂ = 5

difference = d = second term - first term

                        = 5 - 2

                      d = 3

Formula for finding nth term in arithmetic sequence:

   [tex]\sf \boxed{t_n = a + (n-1)*d}[/tex]

     t₈ = 2 + (8 -1) * 3

        = 2 + 7 *3

        = 2 + 21

    t₈ = 23

The line plot shown C in the figure is correct.

Given that the recorded lengths of ribbon pieces which is used in project is [tex]11\frac{1}{4},11\frac{1}{4},10\frac{3}{4},10\frac{1}{2},10\frac{7}{8},10\frac{5}{8},9\frac{7}{8},11\frac{1}{4}[/tex].

Frequency refers to the number of times an event or  value occurs. A frequency table is a table that lists items and shows how many times those items occurred.

A line plot displays the data using a no. line.

Firstly, we will fimd the frequency of each value

Values                               Frequency

9 (7/8)                                        1

10(4/8)=10(1/2)                           1

10(5/8)                                       1

10(6/8)=10(3/4)                          1

10(7/8)                                       1

11(2/8)=11(1/4)                             3

Option A is incorrect because 11(2/8) has no data values in the line plot (i.e. frequency = 0)

Option B is incorrect because 11(2/8) has no data values in the line plot (i.e. frequency = 0)

Option C is correct because the frequency distribution of the data is represented correctly in the line plot.

Option D is incorrect because 11(2/8) has 2 data values in the line plot (i.e., frequency = 2)

Hence, the line plot which correct shows the data is third line plot.

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Answer:

============

Hello to you from Brainly team!

Find z-score using relevant equation:

Substitute values and calculate:

Using the z-score table find the corresponding P- value.

Answer:0.30854

Step-by-step explanation:Solution:

Given:

Using the z-scores formula;

From the z-scores table, the probability is;

Therefore, the probability that the grade is less than 84 is 0.30854

Answer:

7

Step-by-step explanation:

1, 1, 2, 4, 7, 8, 10, 15, 20

median = 7

There are 24 ways in which we can arrange 4 letters of the word "SOLVE" if no letter can be used more than once.

Given a word of 4 letters of the word "SOLVE".

We are required to find the number of ways the four letters of the word SOLVE if no letter can be used more than once.

Permutation is an arrangement of objects in a definite order of things.

Factorial of a number is the product of it and its lesser numbers upto 1.

Number of letters=4

Number of ways=4!

=4*3*2*1

=24 ways

Hence there are 24 ways in which we can arrange 4 letters of the word "SOLVE" if no letter can be used more than once.

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Answer:

60

Step-by-step explanation:

140 = 80 + z

z = 60

Answer:

60°

Step-by-step explanation:

The whole angle is 140° and one side is 80°. Now, you just have to subtract 140 and 80 to get 60. I hope this helps!

Based on the graph of the function (F(x) = log6x), the following facts are true:

A graph is a type of chart that is used to graphically represent data on both the horizontal and vertical lines of a Cartesian coordinate i.e x-axis and y-axis.

By critically observing the graph of the function (F(x) = log6x) attached in the image below, we can infer and logically deduce that its domain and range include all real numbers that are greater than 0 (x > 0).

This ultimately implies that, the following facts are true:

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Complete Question:

Which facts are true for the graph of the function below? Check all that apply. F(x) = log6 x

A. It is increasing.

B. The range is y > 0.

C. The x-intercept is (1, 0).

D. It is decreasing.

E. The y-intercept is (0, 6).

F. The domain is x > 6.

Answer:

(x + 6)(x - 2) = x² + 4x - 12

(x + 2)(x - 8) = x² - 6x - 16

(x + 6)(x - 6) = x² - 36

(x - 5)(x - 1) = x² - 6x + 5

(x - 4)(x - 10) = x² - 14x + 40

(x + 2)(x + 5) = x² + 7x + 10

Step-by-step explanation:

Use FOIL.

(x + 6)(x - 2) =

F - first: x × x = x²

O - outer: -2 × x = -2x

I - inner: 6 × x = 6x

L - last: 6 × -2 = -12

(x + 6)(x - 2) = x² - 2x + 6x - 12

Now, combine like terms.

(x + 6)(x - 2) = x² + 4x - 12

(x + 2)(x - 8) = x² - 6x - 16

(x + 6)(x - 6) = x² - 36

(x - 5)(x - 1) = x² - 6x + 5

(x - 4)(x - 10) = x² - 14x + 40

(x + 2)(x + 5) = x² + 7x + 10

Answer:

slope = - 2

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 4, - 5 ) and (x₂, y₂ ) = (- 2, - 9 )

m = [tex]\frac{-9-(-5)}{-2-(-4)}[/tex] = [tex]\frac{-9+5}{-2+4}[/tex] = [tex]\frac{-4}{2}[/tex] = - 2

Answer:

Step-by-step explanation:

If the lines are parallel, it means that the slopes are the same.  To write an equation in the slope intercept form, we need the slope and the y-intercept.  We are given the slope.  We need to find the y-intercept.  We can use the slope and the point to help us.  The point is written in the form (x,y).  In this case the point is (2,4) so we will use 2 for x and 4 for y.

y = mx + b  Plug in what we know

4 = -4(2) + b  b is what we are looking for.  It is the y-intercept

4 = -8 + b  Now add 8 to both sides

12 = b

Now we can write the equation:

y = -4x +12

Answer: 47°

Step-by-step explanation:

c2 =a2 +b2

that's the rule

for example

c2=5^2+5^2

c2=25+25

c2=50 square root is

c=7.07^2

The following integer values of x satisfy the given inequality,

4, 5, 6, 7, 8

What is an inequality?

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made using inequality.

Solving the Inequality

The given inequality is,

5x + 4 > 19

5x > 19 - 4

5x > 15

x > 15/5

x > 3

So, the required values of x must be greater than 3 in the given interval, [2,8]

Thus, the integer values of x in the the interval [2,8] that satisfy the given inequality are 4, 5, 6, 7 and 8 (∵ Square brackets of an interval denote inclusion of the terminal values).

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The area of the rectangle is 105 square cm

Represent the dimensions of the rectangle with x and y

So, the length of the square would be:

Length = x - 2

Width = y + 6

The areas are then calculated as:

Rectangle = xy

Square = (x -2)(y + 6)

The relationship between the areas is:

(x -2)(y + 6) = 64 + xy

Expand

xy + 6x - 2y - 12 = 64 + xy

This gives

6x - 2y - 12 = 64

Add 12 to both sides

6x - 2y= 76

Divide through by 2

3x - y = 38

By trial by error, we have:

x = 15 and y = 7

The rectangle area is then calculated as:

Rectangle = xy

This gives

Rectangle = 15 * 7

Evaluate

Rectangle = 105

Hence, the area of the rectangle is 105 square cm

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The right triangle whose hypotenuse is the square root of 17 has legs of 1 inch and 4 inches

Step 1 and 2: Create an isosceles right triangle

This is represented by the attached figure in (see figure 1 for this triangle)

The legs of this triangle have a length of 1 inch

Step 3: The hypotenuse

This is calculated using the following Pythagoras theorem

[tex]h^2 = 1^2 + 1^2[/tex]

This gives

[tex]h = \sqrt 2[/tex]

Step 4: Create another isosceles right triangle

This is represented by the attached figure in (see figure 2 for this triangle)

The legs of this triangle are 1 inch and 2 inches, respectively

This hypotenuse is calculated by:

[tex]h^2 = 2^2 + 1^2[/tex]

This gives

[tex]h = \sqrt 5[/tex]

Step 5: Create another isosceles right triangle

This is represented by the attached figure in (see figure 3 for this triangle)

The legs of this triangle are 1 inch and 3 inches, respectively

This hypotenuse is calculated by:

[tex]h^2 = 3^2 + 1^2[/tex]

This gives

[tex]h = \sqrt {10[/tex]

Step 6: Create another isosceles right triangle

This is represented by the attached figure in (see figure 4 for this triangle)

The legs of this triangle are 1 inch and 4 inches, respectively

This hypotenuse is calculated by:

[tex]h^2 = 4^2 + 1^2[/tex]

This gives

[tex]h = \sqrt{[17[/tex]

See that the hypotenuse is the square root of 17

Hence, the right triangle whose hypotenuse is the square root of 17 has legs of 1 inch and 4 inches

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