from a point 1.5 mi from a launcch pad at cape canaveral, an observer sights a space shuttle at an angle of elevation of 10 degrees moments after it is launched. after 10 seconds, the angle of elevation is 50 degrees. how far does the space shuttle travel vertically during the 10 second interval? what is the average speed of the space shuttle during that interval?

By using the fact that the sum of the interior angles of a triangle must be 180°, we will get:

Remember that the sum of the internal angles of a triangle is always equal to 180°, then we can write:

m∠B + m∠C + m∠D = 180°

Then:

13x - 35 + 5x - 19 + 2x + 14 =180

20x -40 = 180

20x = 180 + 40

20x = 220

x = 220/20

x = 11

Now that we know the value of x, we can find the measures of the angles.

m∠B = (13x- 35)° = (13*11 - 35)° = 108°

m∠B = (5x - 19)° = (5*11 - 19)° = 36°

m∠D = (2x + 14)° = (2*11 + 14)° = 36°

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In step 2: the additive property of equality was applied.

In step 4: the division property of equality was applied.

What are the properties to solve equation?

The properties of the relationship of equality, reflexivity, symmetry, transitivity, and the properties of operations are employed to solve an equation.

These characteristics hold true in both propositional language and arithmetic.

The following can be used to sum up this: An equality is still valid if the exact same operation is carried out on both sides of the equality.

Given that:

Step 1: 3x - 10 = -16

The additive inverse of -10 is +10

Step 2: 3x - 10 + 10 = -16 + 10 [Additive inverse]

Step 3: 3x = -6

Step 4: 3x/3 = -6/3  [Division property]

Step 5: x = -2

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Answer: sequences 1,5,7,9,10

Step-by-step explanation:

An arithmetic sequence is defined by a sequence of numbers with a common difference between terms. Technically if x=0 in q9 we have a constant sequence, which by definition is arithmetic. However if x does not equal 0 it is not arithmetic.

The speed of the boat in still water is - 37 km/h

let,  the distance be 'x' km/hr.

And the speed of the boat in still water is 'S' km/hr.

According to the question,

In downstream,

x = ( S + 3 ) * 4.5 ..........(1)

Similarly,

In Upstream,

x = ( S - 3)* 5 ........... (2)

From equations (1) and (2),

  ( S + 3 ) * 4.5 = (S - 3) * 5

or, 4.5 S + 13.5 = 5S -  15

or, 5S - 4.5S = 15 + 13.5

or, 0.5S = 18.5

divide both sides by 0.5,

0r, S = 37

So, the speed of the boat in still water is - 37 km/h

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The force required to accelerate a 0.50kg ball at 2000m/s² is 100 N

The definition of force in physics is: The push or pull on a massed object changes its velocity.

An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude.

Motion is described in physics as a change in position with respect to time. Motion, to put it simply, is the movement of a body. Motion is typically characterized as:

Variation in speed

Change of course

In the given problem the force required to change the body's state is calculated by the formula

F = mass *  acceleration

= 0.5 * 200

= 100 N

the force is 100N

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This method is valid since it produces an interval that contains the true difference 95% of the time. The interval for the gender difference in U.S. teen depression rates is between 3.2% and 8.5%, with girls having higher rates.

The confidence interval method is a valid way of estimating a population parameter based on a sample statistic. In this case, the sample statistic is the 6% difference observed in the study. The confidence interval is used to estimate the true difference between the two groups in the population. This method produces an interval that contains the true difference 95% of the time. In this case, the 95% confidence interval for the gender difference in U.S. teen depression rates is between 3.2% and 8.5%, with girls having higher rates. This means that there is a 95% chance that the true difference in depression rates between boys and girls is somewhere between 3.2% and 8.5%. This method is considered valid because it produces an interval that contains the true difference 95% of the time.The 95% confidence interval for the gender difference in U.S. teen depression rates is calculated as follows:

Lower bound: 6% - 1.96*(Standard Error)

Lower bound: 6% - 1.96*(1.5%)

Lower bound: 3.2%

Upper bound: 6% + 1.96*(Standard Error)

Upper bound: 6% + 1.96*(1.5%)

Upper bound: 8.5%

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Answer:

3x is a single term

Step-by-step explanation:

The "3" is a coefficient. The "x" is the variable. is also a single term.

hope this helps

10-(x+3)/2=8 => correct answer is - 8

=> 10 - (x+2) = 8x2

=> 10 - x - 2 = 16

=> 10 - x = 16 + 2

=> 10 - x = 18

=> -x = 18 - 10

=> x = -8

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The 38 square feet increase in the area of the patio following the increase in the length and width by 2 feet and the 2 square feet increase following the increase in the length by 2 feet and decrease in the width by 2 feet indicates that the area of the patio is 70 square feet.

The area of a plane figure is the space occupied by the figure of a specified surface upon which it is placed.

Let L represent the length of the patio, and let W represent the width of the patio, we get;

Area of the patio = L × W

(L + 2) × (W + 2) = L·W + 2·L + 2·W + 4 = Area + 38

Therefore; (L + 2) × (W + 2) = L·W + 2·L + 2·W + 4 = L × W + 38

2·L + 2·W + 4 = 38 (subtraction property)

2·L + 2·W = 38 - 4 = 34

2·L + 2·W = 34...(1)

(L + 2) × (W - 2) = L·W - 2·L + 2·W - 4 = Area + 2 = L·W + 2

L·W - 2·L + 2·W - 4 - L·W = L·W + 2 - L·W (Subtraction property)

2·W - 2·L - 4 = 2

2·W - 2·L - 4 + 4 = 2 + 4 = 6 (Addition property)

2·W - 2·L = 6...(2)

The simultaneous equations (1) and (2) are solved as follows;

Adding equation (1) to equation (2), we get;

2·L + 2·W + 2·W - 2·L = 34 + 6 = 40

4·W = 40

W = 40 ÷ 4 = 10

W = 10

The width of the patio, W = 10 feet

2·W - 2·L = 6, therefore;

2 × 10 - 2·L = 6

2·L = 2 × 10 - 6 = 14

L = 14/2 = 7

The length of the patio, L = 7 feet

The area of the patio = L × W

L × W = 7 feet × 10 feet = 70 square feet

The area of the patio = 70 square feet

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Answer:

3 and 3/11

Step-by-step explanation:

[tex]\frac{8}{2 \frac{4}{9} } \\\\\frac{8}{ \frac{22}{9} } \\\\= 8 / \frac{22}{9} \\\\= \frac{8}{1} / \frac{22}{9} \\\\= \frac{8}{1} * \frac{9}{22} \\\\[/tex]

[tex]=\frac{72}{22} \\\\= 3 \frac{6}{22} \\\\= 3 \frac{3}{11}[/tex]

Step-by-step explanation:

8 ÷ 2 4/9

so, as always with operations involving fractions I recommend to convert mixed numbers to full fractions first :

2 4/9 = (2×9 + 4)/9 = (18 + 4)/9 = 22/9

the division looks then like this :

8 ÷ 22/9

or

8 / 22/9 = 8/1 / 22/9

remember, when we divide by a fraction, then this is the same as a multiplication with the upside-down fraction :

8/1 × 9/22 = 8×9 / 1×22 = 72/22 = 36/11 =

= (3×11 + 3)/11 = 3 3/11

8 ÷ 2 4/9 = 3 3/11

the symbols ÷, /, : have a little bit different semantic meaning in their context, but they all do the same thing : divide.

and they are therefore interchangeable.

Answer:

Step-by-step explanation:

The amount  Trevor's family spent, in total, on shower water in the past month = 0.03 dollars per minute

In this question we have been given there are 6 people in Trevor's house.

There are 3 bathrooms in the house.

Each person showered for an average of 480 minutes and used an average 72 liters of shower water (over the entire month)

We need to find the amount of money Trevor's family spent, in total, on shower water in the past month.

By unitary method,

72 * 6 = 432 liters of shower water used by the entire family over the month

Each liter costs $0.2

so by unitary method,

the total amount paid:

A = 432 * 0.2

  =  86.4 dollars

Each person showered for an average of 480 minutes.

So, total minutes would be 6x480 = 2880 minutes.

So, the required amount would be,

86.4/2880 = 0.03 dollars  per minute

Therefore, Trevor's family paid $0.03 per minute on shower water.

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To cut the standard error of the mean in half, the sample size must be increased by a factor of four.

Therefore, the answer is False.

The formula to determine the standard error of the mean is

SE = SD/ √n

where SD is the standard deviation

n is the sample size

Therefore the standard error of the mean is inversely proportional to the square root of the sample size. Thus in order to decrease the standard error of the mean to half, we should increase the sample size by a factor of 4.

SE' = SD/ √(4n)

SE' = SD/ 2n

SE' = SE/ 2

--The question is incomplete, answering to the question below--

"To cut the standard error of the mean in half, the sample size must be increased by a factor of two. True or False."

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Step-by-step explanation:

send the question compeletly .

Distributive Property

Addition Property of Equality

Simplifying

Division Property of Equality

Simplifying

To calculate the perimeter of the figure, I first calculated the area and the breadth of each rectangle which is 4/18m2 and 1/9m respectively.

The perimeter of the figure can be calculated by adding the perimeter of each rectangle.

Perimeter = 4 x (2 x (1/9 m) + 2 x (4/18 m))

Perimeter = 8 x (1/9 m + 4/18 m)

Perimeter = 104/18 m

Perimeter = 5.78 m

The figure I made up consists of four identical rectangles that form a square at the center. To calculate the perimeter of the figure, I first calculated the area and the breadth of each rectangle which is 4/18m2 and 1/9m respectively. As the four rectangles are identical, I multiplied the perimeter of one rectangle by 4 to get the perimeter of the entire figure. Perimeter of one rectangle is calculated by adding the length and breadth of the rectangle. I multiplied the sum of the length and breadth of a rectangle (1/9 m + 4/18 m) by 8 to get the perimeter of the figure. Finally, I simplified the result to get the perimeter of the figure which is 5.78 m.

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The solution for the quadratic equation; x squared + 8 x + 16 = 0 as required to be determined using a numerical approach is; Choice C; x = -4.

It follows from the task content that the solution of the quadratic equation is to be determined by using a numerical approach as stated.

On this note, since the standard form quadratic equation takes the form; ax² + bx + c = 0.

To solve, it is important to determine two numbers whose product yields c and sum is; b.

Therefore, for the equation; x² + 8x + 16 = 0; the numbers are; 4 and 4.

Therefore, we have;

x² + 4x + 4x + 16 = 0.

x (x + 4) + 4 (x + 4)

(x + 4) (x + 4) = 0

x = -4.

On this note, the correct answer choice is; Choice C; x = -4.

Complete question; The correct question syntax is; x² + 8x + 16 = 0.

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Step-by-step explanation:

what equations do we really have here ?

there seem to be typos in the equations.

I assume you truly have

x + 3y = 12

-5x + y = -12

now, elimination means that we multiply the equations (both sides to keep the equations in their information unchanged) by applying factors and then add the resulting equations.

the result should have "eliminated" one of the variables, so that we can solve for the remaining variable.

and then we use that result and one of the original equations to solve for the second variable.

in our case I suggest we try to eliminate x first.

so, we multiply the first equation by 5. the second equation can stay as it is.

and then we add both :

5x + 15y = 60

-5x + y = -12

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

0 16y = 48

y = 48/16 = 3

using e.g. the original first equation :

x + 3y = 12

we put in the already calculated value for y (3) and solve for x :

x + 3×3 = 12

x + 9 = 12

x = 12 - 9 = 3

x = 3

y = 3

you understand the principle ? please let me know, if you have further questions.

if your actual equations are different to my assumptions, you need to apply this in the same way as I showed you here to whatever the real equations are.

Answer:

  (x, y) = (3, 3)

Step-by-step explanation:

You want to solve by elimination the system of equations ...

The point of the elimination method is to combine the equations in a way that causes the coefficient of one of the variables to become zero. In general, this can be accomplished by multiplying each equation by the coefficient of the chosen variable in the other equation, then subtracting the results one from the other.

Considering the x-coefficients, we can multiply the first equation by -5, the second by 1 and subtract the first product from the second. This eliminates the x-variable.

  1(-5x +y) -(-5)(x +3y) = 1(-12) -(-5)(12)

  -5x +y +5x +15y = -12 +60 . . . . . . . . . . eliminate parentheses

  16y = 48 . . . . . . . . . . . . . . . . . . . collect terms

  y = 3 . . . . . . . . . . . . . . . . divide by 16

Now, we need to find x. We can do this by substituting for y in either equation. We choose to use the first equation:

  x + 3(3) = 12

  x = 3 . . . . . . . . . . subtract 9

The solution to the system of equations is (x, y) = (3, 3).

__

Additional comment

We chose to explain the elimination in terms of subtraction. That subtraction can be done in either order:

  -5(equation 1) -1(equation 2)

or

  1(equation 2) -(-5)(equation 1)

We chose the latter order so the coefficient of y would end up positive. We find fewer mistakes are made when the signs are positive.

Your curriculum materials may explain the elimination process in terms of addition. You may have noticed that subtracting -5 times the first equation is the same as adding 5 times the first equation. When you do this using addition, one of the multiplier coefficients needs to be the opposite of the coefficient of the variable in the other equation.

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Answer: 6 1/2. yards

Step-by-step explanation:    you have to add 1 1/3 + 5/6, which is 2 1/6. 2 1/6x3=6 1/2.  then thats your answer

If a credit card has an average daily balance of $1250 and the annual interest rate is 18%, the total bill for the month will be $1,268.75.

The average daily balance is the quotient resulting from the summation of the card's daily balances and the division by the number of days in the billing cycle.

The finance charge, which represents the interest and other fees for the use of the credit card, is computed by applying the monthly percentage rate (MPR) on the average daily balance.

Average daily balance = $1,250

Annual interest rate = 18%

Monthly percentage rate = 1.5% (18% ÷ 12)

Finance charge = $18.75 ($1,250 x 1.5%)

Total bill for the month = Average daily balance + Finance charge

= $1,268.75 ($1,250 + $18.75)

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Answer: C) $3,780.00

Step-by-step explanation:

1 year = 7% interest rate

3 years = 21% interest rate

21% = 0.21

Take 18000 times 0.21 = $3,780.00

The maximum km's you travel if your cost is not more than Birr 1350. is 130 kilometers.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

From the information, the ride service charges Birr 50 to pick you up from the hotel and Birr 10 per km for the trip.

Let the number of kilometers be x.

50 + 10x = 1350

Collect the like terms

10x = 1350 - 50

10x = 1300

Divide

x = 1300 / 10

x = 130

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The first derivative of quadratic function is obtained as a linear function.

The differentiation of a function is defined as rate of change of its value at a point. It can be written as f'(x) =  lim h --> 0 (f(x + h) - f(x)) /(x + h - x).

It can also be described as the slope of the tangent of function at a given point.

The general form of a quadratic function is as below,

f(x) = ax² + bx + c

Its first derivative can be written as below,

f'(x) = 2ax + b

The degree of the function f'(x) is 1.

Thus, it is a linear function.

Hence, the function to describe the derivative of quadratic function is linear.  

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The probability that both candies are of same color is 0.22

Probability:

                Probability means possibility.The value is expressed from zero to one.In other words probability is simply how likely something is to happen.

The distribution of colors of candies in a bag is as follows.

    Brown      0.1

    Red         0.3

   Yellow      0.2

   Green      0.2

   Orange    0.2

The probability for both candies are Orange.

                = 0.2 x 0.2

                = 0.04

The probability for both candies are Brown.

               =  0.1 x  0.1

               = 0.01

The probability for both candies are Yellow.

               = 0.2 x 0.2

               = 0.04

The probability for both candies are Green.

              = 0.2 x 0.2

              = 0.04

The probability for both candies are Red.

             = 0.3 x 0.3

             = 0.09

Now,

       The total probability  that they are the same color

                    = 0.04 + 0.01 + 0.04 + 0.04 + 0.09

                    = 0.22

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Answer:

No solution

Step-by-step explanation:

x=12.0; y=19.6

Option 4 is the right answer.

What are the properties of tangent of the circle?

A tangent is correctly formed only if touches the circle at only one point. A tangent never passes through a circle, that is, it never crosses the circle while entering its interior. A tangent is also not known for intersecting the circle at the two different points.

Since, in a circle the radii are equal.

So, OA=OB=x=12

Tangent to a circle is the line that touches the circle at only one point.

The length of tangents from an external point to a circle are equal.

By the theorem,

If two tangents are drawn from an external point of the circle, then they are of equal lengths.

So, AC =BC (by the theorem)

AC and BC look to be tangents- tangents to a circle from a point are congruent.

So, AC is congruent to BC.

Thus, AC=BC=y=19.6

Hence, x=12.0 and y=19.6

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Answer:

B. Alternate exterior angles

Step-by-step explanation:

Alternate exterior angles are angles opposite outside of each other and have the same degree. So the answer is B