The angle of depression from the top of Pike’s Peak, at an altitude of 14,000 feet, to the city of Colorado Springs is 8o. The horizontal distance from the city to the peak is 58,000 feet. Find the altitude of Colorado Springs.

Answer:

Step-by-step explanation:

the volume of top triangular prism :

(16x21)/2x15=2520 yd^3

the volume of bottom:

22x16x15=5280 yd^3

so the volume of the figure:

2520+5280=7800 yd^3

The measure of the major arc along the perimeter of the circle between Stanley and Frank is 264°.

A circle's arc, or circumference, is a section of the circle. The difference between an arc length and an arc measure is the angle the arc creates with the circle's center. It is possible to measure this arc in radians or degrees.

Given:

Fifteen friends are playing Duck, Duck, and Goose.

The friends sit equally spaced in a circle.

So, 360/15 = 24° is the angle measure of an arc.

There are three people between Stanley and Frank.

That means there are 11 people between Stanley and Frank.

So, 11 x 24 = 264° is the measure of the major arc.

And the perimeter of the major arc is 264°

Therefore, the perimeter of the major arc is 264°

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[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{1}~,~\stackrel{y_1}{5})\qquad B(\stackrel{x_2}{4}~,~\stackrel{y_2}{2})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AB=\sqrt{(~~4 - 1~~)^2 + (~~2 - 5~~)^2} \implies \implies AB=\sqrt{( 3 )^2 + ( -3 )^2} \\\\\\ AB=\sqrt{ 9 + 9 } \implies AB=\sqrt{ 18 }\implies AB\approx 4.24[/tex]

now, we could do the same thing for CD,  however, notice, the y-coordinates are the same, meaning is just a horizontal line, we can just count the units off the grid, from 2 to 6, 4 units.

Answer:

208,000

Step-by-step explanation:

The ages of the five family members as required are; 3, 10, 13, 42 and 42.

As evident, in the task content, let a, b , c , d , e represents the ages of the family members in ascending order.

Since the median of the ages is; 13, it follows that the the third term, c = 13.

Also, since the mode is 42, it follows that; d = e = 42.

Also, since the range of the ages is 39, it follows that; 42 - a = 39 and consequently a = 3.

Finally, since the mean age is 22; it follows from the mean formula that;

22 = ( 3 + b + 13 + 42 + 42 ) / 5

110 = b + 100

b = 10.

Ultimately, the ages of the five family members as required are; 3, 10, 13, 42 and 42.

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Two different values are possible for the length of Rectangle jklm.

When we say that two rectangles are congruent, we indicate that their sides are equal. The rectangles' lengths and widths have to be comparable. It's feasible that jm will be 4 or 7 inches long given that one rectangle has dimensions of 4 and 7. Two lengths are conceivable as the solution. The length and breadth make up the rectangle shape. A rectangle has four sides, and its opposing sides are all the same length. You are given the perimeter of a rectangle. The perimeter, as you know, is the total distance along the outside of the rectangle.

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The number of passes that John has attempted this year will be 500.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

John is a quarterback. This year, he completed 350 passes, which is 70% of all the passes he's attempted this year.

Let 'y' be the total passes that John attempted. Then the equation is given as,

0.70 = (350 / y)

y = 350 / 0.70

y = 500

The number of passes that John has attempted this year will be 500.

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The model [tex]p = 200.3^d[/tex] satisfies the statement, A population of cells starts at 200 and triples every day.

The formula for exponential growth is [tex]y = y_0.e^{(kt)}.[/tex]

The formula for exponential decay is [tex]y = y_0.e^{(-kt)}.[/tex]

Given, A population of cells starts at 200 and triples every day.

Where 'p' is the number of cells and 'd' is the number of days.

The situation is represented by [tex]p = 200.3^d[/tex].

Now, Three times 200 is 600 and Nine times 200 is 1800.

At d = 1.

[tex]p = 200.3^1[/tex].

[tex]p = 600[/tex].

And,

At, d = 2.

[tex]p = 200.3^2[/tex].

[tex]p = 1800[/tex].

So, The model satisfies the statement and it is true.

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The population of the bees when it was first measured was 500 bees

The bees are  growing by the same factor each week. The answer is yes

At the fist time the bees where measured, we have to measure from the origin of the graph.

The first point on the graph is at the population of 500

2. To get if the growth is by the same factor, we have to observe how the growth is taking place weekly

In the first week, it grew from 500 to 1000

1000 / 500 = 2

In the second week, the growth is from 2000 to 1000

2000 / 1000 = 2

In the third week. the growth is from 2000 to 4000

4000 / 2000 = 2

Hence there is a growth constant of 2 across the weeks

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The bedroom has a surface space of 17.4225 m² and the closet has a surface area of 2.5875 m².

In mathematics, the area is a measure of the amount of two-dimensional space taken up by a shape. It is a scalar quantity, meaning it has only magnitude and no direction. The unit of measurement used for area depends on the units used for the length of the sides of the shape. Common units used to measure area include square centimeters, square meters, square inches, and square feet. The formula for finding the area of a shape depends on the specific type of shape. For example, the area of a rectangle is given by the formula A = lw, where l is the length and w is the width of the rectangle. The area of a triangle is given by the formula A = (1/2)*bh, where b is the base and h is the height of the triangle.

Here,

area of bedroom=l*w

l=5.05 m

w=3.45 m

area of bedroom=5.05*3.45

=17.4225 m²

area of closet=l*w

l=0.75 m

w=3.45 m

area=0.75*3.45

=2.5875 m²

The area of the bedroom is 17.4225 m² and that of closet is 2.5875 m².

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According to the information, the line plots of points 6 and 7 have several values that are repeated more than once as shown in the graphs.

To make a line plot we must identify the values that we must locate on the number line. Once we know the values we must place a point or symbol above the corresponding numerical value. For each number we must put a point, so we can count the frequency of different values.

Based on the above, we can infer that the line plots of points 6 and 7 would look like this:

attached images

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The numerical values of x and y are 14 and 54 respectively.

The sum of angles on a straight line is equal to 180 degrees.

From the diagram, angle (9x + 2)° and angle (5x - 18)° are on a straight line,

Since the sum of angles on a straight line is equal to 180 degrees.

(9x + 2)° + (5x - 18)° = 180°

Solve for x

9x + 2 + 5x - 18 = 180

14x - 16 = 180

14x = 180 + 16

14x = 196

x = 196/14

x = 14

Now, angle (9x + 2)° and angle (2y + 20)° are corresponding angles.

Since corresponding angles are congruent.

(9x + 2)° = (2y + 20)°

Plug in x = 14 and solve for y

9( 14 ) + 2 = 2y + 20

126 + 2 = 2y + 20

128 = 2y + 20

128 - 20 = 2y

108 = 2y

2y = 108

y = 108/2

y = 54

Therefore, the value of x is 14 and y is 54.

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The exponential equation is N ( t ) = a ( b )^t , where a = 50 and b = 3

The exponential growth or decay formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

x ( t ) is the value at time t

x₀ is the initial value at time t = 0.

r is the growth rate when r>0 or decay rate when r<0, in percent

t is the time in discrete intervals and selected time units

Given data ,

Let the number of bacteria in the culture at a given time be N ( t )

The culture increases by a factor of 2

So , the value of r = 200 % , r = 2

Now , when t = 0 , the number of bacteria in the culture N ( 0 ) = 50

So , the exponential equation is

N ( t ) = N ( 0 ) ( 1 + r )^t

Substituting the values in the equation , we get

N ( t ) = 50 ( 1 + 2 )^t

N ( t ) = 50 ( 3 )^t

On simplifying the equation , we get

N ( t ) = a ( b )^t , where a = 50 and b = 3

Hence , the exponential equation is N ( t ) = 50 ( 3 )^t

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1 cm is defined as 1/100 of a meter. One foot is defined as 1/3 of a yard or 12 inches in length. We know that, 1 inch = 2.54 cm and therefore, 23.5 centimeter = 9.252 inches

Centimeters :

The centimeter (cm) is the fractional part of the meter, the international standard unit of length, and equals approximately 39.37 inches. It is defined as 1/100 of a meter.

The centimeter is based on the SI unit of measurement and is equal to one hundredth of a meter as indicated by the prefix "centi". The metric prefix ranges from 10-18 to 1018 in decimal, and the base (metric in this case) has no prefix and a modulus of 1. Exploring the most commonly used metric prefixes such as kilogram, mega, giga, tera, centi, milli, micro, and nano can be useful for quickly navigating metric units.

Inch:

Inches is a unit of length or distance in several systems of measurement, including traditional American units and British Imperial units. An inch is defined as 1/12 of a foot, so 1/36 of a yard. By modern definition, 1 inch equals 25 exactly 4 mm.

The term "inch" comes from the Latin unit "uncial", equivalent to "1/12" in Roman terms. There were several standards for inches in the past and the current definition is based on international yards. One of the earliest definitions of an inch was based on a barley grain, where an inch equals the length of three dry round grains of barley laid end to end. Another version of the inch is believed to be derived from the width of a person's thumb, where length was obtained by averaging the widths of three thumbs (small, medium, and thumb).

By multiplying  the value in centimeters by the conversion factor 0.3937007874021.

So, 23.5 centimeters = 23.5 × 0.39370078740213

                                   = 9.25196850395 inches.

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The tax money given by Andy is equivalent to $151.83.

Tax is a type of financial charge imposed by governmental organization on the individual to fund government spending and various public expenditures.

Given is that a bike shop in Belleville bought a mountain bike for $723 and marked it up 50% from the original cost.

Total cost of bike after marking it up -

{x} = $723 + ${50% of 723}

{x} = $723 + ${50/100 x 723)

{x} = $723 + $361.5

{x} = $1084.5

Money given by Andy as tax -

{t} = 14% of 1084.5

{t} = 14/100 x 1084.5

{t} = $151.83

Therefore, the tax money given by Andy is equivalent to $151.83.

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Answer:

There is exactly one solution: (1, 2).

Step-by-step explanation:

For this, it's already in slope intercept form so all you have to do is graph the two and see at what point do these two lines cross, which is (1, 2).

Hope this helps!

Answer:

Step-by-step explanation: 9.17

Calculating antiderivatives, definite line integrals, double and triple integrals, and improper integrals is made easy using Wolfram | Alpha.

Wolfram| | Alpha does integral computations differently than people. It uses the Integrate function in Mathematica, which is the result of much mathematical and computational study. Integrate does integrals differently than individuals do. Instead, it makes use of robust, broad algorithms, which frequently need quite complex arithmetic. One includes determining an integral's general form, differentiating this form, and then resolving equations to match ambiguous symbolic parameters. The equations produced in this technique can be quite complicated, even for relatively basic integrands, and are best solved using Mathematica's robust algebraic computation capabilities. Converting integrals to generalized hypergeometric functions and then using collections of relations about these extremely complex mathematical functions is another method Mathematica utilizes to calculate integrals.

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Answer:

4

Step-by-step explanation:

2x4=8, 8+11=19

Answer:

Goku died you I just started watching

In calculus, 0^0 is an indeterminate form. It is not equal to infinity. But 0x0 is equal to zero.

Some of the indeterminate forms 0/0, 0×∞,∞/∞, ∞ −∞, ∞/0, [tex]0^{0}[/tex].

An unknown value is referred to as being "indeterminate." Even after inserting the limits, we are still unable to determine the original value, according to the indeterminate form of mathematics. When two functions are considered as a ratio, the indeterminate form frequently appears when both functions go closer to 0 in the limit. The term "indeterminate form 0/0" refers to these circumstances. The indeterminate form can also be created, much as addition, subtraction, multiplication, and exponential operations. If the limiting behavioral of separate components of the provided expression cannot identify the overall limit, a limit is said to be indeterminate.

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The equation of line is y= -1/4x+ 6.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

passes through the point (4, 5);

slope = -1/4

Using the slope intercept form

y = mx + b

y= -1/4x + b

As the point passes through (4, 5) then

5 = -1/4 (4) + b

5 + 1 = b

b= 6

So, the equation of line is y= -1/4x+ 6.

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Answer:

Liberty Hill

Step-by-step explanation:

To determine which hill is the steepest, calculate the absolute value of m for each hill and compare them:

|m|= |Slope (or gradient)|

    = |[tex]\frac{VerticalDistance}{HotizontalDistance}[/tex]|

The hill with the greatest absolute value of m is the steepest:

|[tex]m_{Dixie} = |\frac{40}{80}|[/tex]

            = 0.5

[tex]|m_{Bell}| =|\frac{20}{80}|[/tex]

          = 0.25

[tex]|m_{Liberty}| = |\frac{60}{80}|[/tex]

               = 0.75

Liberty Hill has the greatest absolute value of m of 0.75, therefore it is the steepest

From the given information, by doing unit conversion 20 ounces is equal to approximately 1.25 pounds.

Unit conversion is the process of converting a given quantity from one unit of measurement to another. It involves using conversion factors or conversion equations to change the numerical value of the quantity while keeping the physical quantity constant. Common units of measurement include length, mass, volume, time, temperature, and many others.

To convert ounces to pounds, you can use the following conversion formula:

1 lb = 16 oz

So, to convert 20 ounces to pounds, you can divide 20 by 16:

20 oz ÷ 16 oz/lb = 1.25 lb (rounded to two decimal places)

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The equation of the line that has a slope of -4 and passes through the point (4, -1) is y = -4x + 15.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of a line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

Given:
An equation,

y = x/4 - 2.

The slope of the line that is perpendicular to the line y = x/4 - 2 is,

= -(1/1/4)

= -4.

The equation of the line that has a slope of -4 and passes through the point (4, -1) is,

y + 1 = -4(x - 4)

y = -4x +16 -1

y = -4x + 15

Therefore, the equation is y = -4x + 15.

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A linear function has a constant rate of change, which means that the change in the value of y is proportional to the change in the value of x. This means that if we plot the points (x,y) for a linear function, they will fall on a straight line.

To determine which of the tables represents a linear function, we can calculate the rate of change between the points. If the rate of change is the same for all pairs of points, then the table represents a linear function.

For the first table:

Rate of change between (−2,4) and (−1,1) = (1−4)/(−1−(−2)) = −3

Rate of change between (−1,1) and (0,−2) = (−2−1)/(0−(−1)) = −3

Rate of change between (0,−2) and (1,−5) = (−5−(−2))/(1−0) = −3

Rate of change between (1,−5) and (2,−8) = (−8−(−5))/(2−1) = −3

Since the rate of change is constant (equal to −3) for all pairs of points, the first table represents a linear function.

For the second table:

Rate of change between (−2,4) and (−1,1) = (1−4)/(−1−(−2)) = −3

Rate of change between (−1,1) and (0,0) = (0−1)/(0−(−1)) = 1

Rate of change between (0,0) and (1,1) = (1−0)/(1−0) = 1

Rate of change between (1,1) and (2,4) = (4−1)/(2−1) = 3

Since the rate of change is not constant (it changes from −3 to 1 to 3), the second table does not represent a linear function.

For the third table:

Rate of change between (2,−2) and (2,−1) is undefined since x does not change.

Rate of change between (2,−1) and (0,0) = (0−(−1))/(0−2) = 0.5

Rate of change between (0,0) and (2,2) = (2−0)/(2−0) = 1

Rate of change between (2,2) and (2,−2) is undefined since x does not change.

Since the rate of change is not constant (it changes from undefined to 0.5 to 1 to undefined), the third table does not represent a linear function.

For the fourth table:

Rate of change between (0,−2) and (1,1) = (1−(−2))/(1−0) = 3

Rate of change between (1,1) and (2,0) = (0−1)/(2−1) = −1

Rate of change between (2,0) and (3,1) = (1−0)/(3−2) = 1

Rate of change between (3,1) and (4,−2) = (−2−1)/(4−3) = −3

Since the rate of change is not constant (it changes from 3 to −1 to 1 to −3), the fourth table does not represent a linear function.

Therefore, the only table that represents a linear function is the first one.

Answer: Yes

Step-by-step explanation:

We don't know the value of n and you are subtracting it from both sides.

Answer: Can't help I tried to figure it out, but it was wrong.

Step-by-step explanation: I'm sorry.

The second and fourth graphs represent linear functions.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

To determine which of the given graphs represents a linear function, we need to check whether the graph is a straight line.

The first graph passes through the points (-3, 0), (-1, -4), and (1, 0). We can plot these points and see that they do not lie in a straight line. Therefore, the first graph does not represent a linear function.

The second graph passes through the points (-4, 0), (0, -4), (4, 0), and (0, 4). We can plot these points and see that they do lie on a straight line. Therefore, the second graph represents a linear function.

The third graph passes through the points (-4, -2), (-4, -1), and (-4, 0). We can plot these points and see that they lie on a vertical line. Therefore, the third graph does not represent a linear function.

The fourth graph passes through the points (-4, 0), (-2, -1), and (0, -2). We can plot these points and see that they do lie on a straight line. Therefore, the fourth graph represents a linear function.

Therefore, the second and fourth graphs represent linear functions.

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Answer: It is the second one

Step-by-step explanation:

Because It makes the most sense