The population of a particular country was 23 million in 1981; in 1987, it was 32 million. The
exponential growth function A =23ekt describes the population of this country t years after 1981. Use
the fact that 6 years after 1981 the population increased by 9 million to find k to three decimal places.

The point of tangency and the equation of the tangent line are (x, y) = (- 5, 0) and x = - 5, respectively. (Correct choice: D)

A figure representing a circle and a tangent line, from which we need to determine the point of tangency and the equation of the tangent line. The point of tangency is a point where the tangent line and the circle meet each other.

Thus, by direct inspection, we have the following results:

Point of tangency

(x, y) = (- 5, 0)

Tangent line

x = - 5

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The circumference of the circle is 50.272in and the area is 3.142 x 8² = 200.96in².

The formula for circumference of a circle is given as:

  C = 2[tex]\pi[/tex]r

where r is the radius

and [tex]\pi[/tex] is 3.142

Area of a circle is given as:

   A = [tex]\pi r^{2}[/tex]

From the diagram,

diameter (d) given is 16in i.e:

d = 16in

but

r = d/2 = 16/2 = 8in

Now solve the C and A using the formula above:

C = 2 x 3.142 x 8 = 50.272in (approx.)

A = 3.142 x 8² = 200.96in² (approx.)

Briefly, a circle is a two-dimensional geometric shape consisting of all points in a plane that are a fixed distance, called the radius, from a given point called the center.

The distance around the circle, also known as its perimeter, is called the circumference.

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The volume of 8 rectangular prism stacked base to base is 2560 in³.

Volume is a measure of three-dimensional space.

To calculate the volume of 8 rectangular prism stacked base to base, we use the formula below

Formula:

Where:

From the question,

Given:

We find the value of h using the formula for the surface area of a prism

Given:

Substitute these values into equation 2

Finally, we subtitute into equation 1

Hence the volume is 2560 in³.

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The fraction of the cookies that are peanut butter cookies is 1/5

From the question, we have the following parameters that can be used in our computation:

Total = 10

Peanut butter = 2

using the above as a guide, we have the following:

Fraction = Peanut butter /Total

So, we have

Fraction = 2/10

Evaluate

Fraction = 1/5

Hence, the fraction is 1/5

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The equivalent area of the parallelogram is 44.4m^2

The formula for finding the area of a parallelogram is expressed as:

Area = base * height

Given the following parameters

Base = 12m

Height = 3.7m

Substitute the given parameters into the formula to have:

Area = 12m * 3.7m

Area of the parallelogram = 44.4m^2

Hence the area of the parallelogram given is 44.4m^2

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The function is invertible and the inverse of the function is y = -3 + √[ (x + 4)/-2]

From the question, we have the following function that can be used in our computation:

y=-2(x+3)^2-4

Swap the variables x and y

So, we have

x = -2(y + 3)^2 - 4

Add 4 to both sides

-2(y + 3)^2 = x + 4

Divide both sides by -2

(y + 3)^2 = (x + 4)/-2

Take the square root and subtract 3 from both sides

y = -3 + √[ (x + 4)/-2]

This represents the inverse of the function

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A better prediction in the scatter plot when for x when y = 7 would be

A scatter plot, аlso known as a scatter diagram or scatter grаph, is a grаphical representаtion оf dаtа thаt displays thе relаtionship between twо variables.

It is used to investigate thе сorrelation or relаtionship between twо quantitativе variables, tyрically rеprеsеntеd on thе x-axis and y-aхis оf a Сartesian cооrdinate system.

In the coordinate Cartesian system shown, for y = 7 the value closest is 11.  x = 52 is far away and will correspond to higher vales of y.

The relationship is a positive association

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B) gas mileage decreases with increase of car weight.

Answer:

x=9 y=-2

Step-by-step explanation:

Substitute -2 for y in x+2y=5

x+2y=5

x+(2)(-2)=5

x-4=5(add 4 to both sides)

x=9

y=-2 as stated before

x=9 y=-2

The values of x, y and z in the given simultaneous equation is:

x = 4

y = 6

z = -3

The 3 simultaneous equations are given as:

x + 7y - z = 49

2x - 5y + 2z = -28

x - 6y=-32

Rearranging the first equation  gives:

x = 49 - 7y + z

2x - 5y + 2z = -28

x - 6y = -32

Substitute 49 - 7y + z into equations 2 and 3 to get:

2(49 - 7y + z) - 5y + 2z = -28

49 - 7y + z - 6y = -32

Convert the equation in terms of u and solving simultaneously gives:

y = 6 and z = -3

Thus:

x = 49 - 7(6) + (-3)

x = 4

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If a load of 10 tons was distributed equally among 6 trucks, each truck would carry 1.6667 tons.

In Mathematics, the unit rate is sometimes referred to as unit ratio and it can be defined as the quantity of material that is equivalent to a single unit of product or quantity.

In order to determine the unit rate, we would use the following mathematical equation (formula);

Unit rate = Number of ounces/Number of trucks

Unit rate = 10/6

Unit rate = 1.6667 tons.

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Complete Question:

A load of 10 tons was distributed equally among 6 trucks, how many does each truck carry?

The expression for h(x) is,

⇒  h (x) = √(x - 2) + 4

Now, Given that;

Initially the graph f (x) is shifted horizontally to the right.

When the graph shifts to right the function then becomes

f (x) → f (x-b)

Where b is the units by which it is shifted towards right .

So, in the figure we can see that it is shifted 2 units to the right .

So, f(x) → f(x-2)

Since f(x) is,

⇒ f (x) = √x

So, f (x-2) = √x - 2

Now, the new obtained graph is again shifted vertically upward

When the graphs shifts upward;

⇒ f(x) → f(x) + b

where b is the units by which it is shifted upward

So, our obtained f(x-2) when shifted upward by 4 units so using the above given transformation of upward shift

i.e. f(x) → f(x) + b

So, Our new graph h(x) = f(x-2) + 4

⇒  h (x) = √(x - 2) + 4

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The steps to graph the absolute value functions are given below.

We have,

Absolute value functions of form f(x) = |ax + b| have a characteristic shape, which depends on the values of a and b.

Here are some general guidelines for graphing these functions:

Find the y-intercept:

To find the y-intercept of the graph, set x=0 and solve for y.

This gives f(0) = |b|, so the y-intercept is at the point (0,|b|).

Find the x-intercept(s):

To find the x-intercepts of the graph, set y = 0 and solve for x.

If b > 0, there are two x-intercepts: x = -b/a and x = b/a.

If b = 0, there is one x-intercept at x=0.

If b < 0, there are no x-intercepts.

Determine the direction of the graph:

If a > 0, the graph opens upwards, like a "V".

If a < 0, the graph opens downwards, like an upside-down "V".

Determine the vertex:

The vertex is the point where the graph changes direction.

If a > 0, the vertex is at (-b/a, 0).

If a < 0, the vertex is at (b/a, 0).

Sketch the graph:

Use the information above to sketch the graph of the absolute value function.

Plot the y-intercept, the x-intercept(s), and the vertex, and then draw a smooth curve connecting these points.

Thus,

The graph of the absolute value functions is given above.

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Answer:5.6

Step-by-step explanation:

28 divided by 5 is 5.6

Answer: $33.6

Step-by-step explanation: 28(.20) will give us our $5.6 discount. now add that on top of 28.

Answer:

James Abbott McNeill Whistler's Nocturne in Black and Gold: The Falling Rocket (c. 1875) is an example of "art-for-art's sake" of the Aestheticism movement.

Answer:

y = 3/2x + 3

Step-by-step explanation:

The slope-intercept form is y = mx + b

2y − 3x = 6

2y = 3x + 6

y = 3/2x + 3

So, the answer is y = 3/2x + 3

Answer:

  132175.2 cm³

Step-by-step explanation:

You want the volume of a sphere with radius 31.6 cm.

The volume of a sphere is given by the formula ...

  V = 4/3πr³

For a radius of 31.6 cm, we find the volume to be ...

  V = 4/3π(31.6 cm)³ ≈ 132,175.2 cm³

The volume of the sphere is about 132,175.2 cm³.

The bearing of the airport from the plane is 245°

The bearing of a point from a location is given by the angle in degrees of rotation from the Northern direction of the location to the direction of the location of the point

The given bearing of the plane from the airport = 65°

Therefore, the direction of the plane from the Northern direction of the airport = 65°

From the Northern direction of the plane, the bearing of the airport = 245°

Hence, the bearing of the airport from the plane is 245°

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9 divided by 11.91 rounded to the nearest hundredth is: 0.76

To show that two numbers are divided, we can add a division sign '÷' between them. So, for example, if we have to show 36 divided by 6, we can write it as 36 ÷ 6. We can also show it in a fraction form as 36/6.

We want to find 9 divided by 11.91 . Thus, this can be expressed as:

9/11.91

where:

9 is the dividend

11.91 is the divisor

Using calculator, we have:

9/11.91 = 0.76

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Answer:non linear

Step-by-step explanation: since the exponent is greater than 1

Edouard Manet's Luncheon on the Grass was shown in the Salon des Refuses after it was rejected for the annual salon.

Option D is the correct answer.

We have,

Edouard Manet's painting "Luncheon on the Grass" was first rejected by the Paris Salon in 1863, as it was considered scandalous due to the nudity of the female figure in the painting.

In response to this rejection,

Emperor Napoleon III ordered an exhibition to be held for all the rejected paintings, which was known as the Salon des Refusés (Salon of the Refused).

Thus,

Edouard Manet's Luncheon on the Grass was shown in the Salon des Refuses after it was rejected for the annual salon.

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Answer:

Step-by-step explanation:

You want to know the number of hours Liz worked at each job, when the total pay for a total of 28 hours work was $175.80. Job A paid $6 per hour, and job B paid $6.60 per hour.

We can let 'b' represent the number of hours worked at job B. Then (28-b) is the number of hours worked at job A. Liz's total pay was ...

  6(28 -b) +6.60(b) = 175.80

Simplifying the equation gives ...

  0.60b +168.00 = 175.80

  0.60b = 7.80 . . . . . . . . . . . subtract 168

  b = 13 . . . . . . . . . . . . . . divide by 0.6

  28-b = 28-13 = 15 . . . hours at Job A

Liz worked 15 hours at Job A, and 13 hours at Job B.

__

Additional comment

Here, we used one equation. If you use two equations, you can get this same equation by substituting for the variable representing hours at Job A. Letting the variable represent hours at the higher-paying job generally results in arithmetic using positive numbers. If you write the equation for the hours at Job A, negative numbers will usually be involved. Though it shouldn't, sometimes that causes confusion.

A graphing calculator may offer two or three ways (or more) you use to can solve the equations. One of them is illustrated in the attachment. It solves the equations ...

The volume of a cylinder whose diameter measures 2.5 cm and has a height of 15.5 cm is equal to 76.10 cubic centimeters.

In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

Note: Radius = diameter/2 = 2.5/2 = 1.25 cm.

By substituting the parameters, we have:

Volume of cylinder, V = 3.142 × 1.25² × 15.5

Volume of cylinder, V = 76.10 cubic centimeters.

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Complete Question:

Calculate the volume of a cylinder whose diameter measures 2.5 cm and has a height of 15.5 cm.

The numeric value of f(x) at x = π/5 is given as follows:

f(π/5) = - 2π/5 - 2

We are given the second derivative of the function, as follows:

f''(x) = -25sin(5x).

As we have the second derivative of the function, the function itself is obtaining integrating the second derivative twice.

Using integral by substitution, the first derivative is given as follows:

f'(x) = 5cos(5x) + K1

In which K1 is the constant.

When x = 0, f'(0) = 3, hence the value of K1 is obtained as follows:

3 = 5 + K1

K1 = -2.

Hence:

f'(x) = 5cos(5x) - 2.

Integrating again, the function is given as follows:

f(x) = 5sin(5x) - 2x + K2.

When x = 0, y = -2, hence the constant K2 is obtained as follows:

K2 = -2.

Thus the function is:

f(x) = 5sin(5x) - 2x - 2.

The numeric value of the function at x = π/5 is obtained as follows:

f(π/5) = 5sin(5(π/5)) - 2(π/5) - 2.

f(π/5) = 5sin(π) - 2π/5 - 2

f(π/5) = - 2π/5 - 2 -> as sin(π) = 0.

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Answer:

The 80.6 square foot roll is less expensive per square foot since it costs $0.03/square foot compared to the other which costs $0.02/square foot

Step-by-step explanation:

Because the question asks which of the two paper towel rolls is less expensive per square foot, we must find the unit rate of both rolls (specifically, cost per 1 square foot)

We can find the unit rate using a proportion:

53.7 square foot roll

[tex]\frac{1.49}{53.7}=\frac{x}{1} \\1.49=53.7x\\0.0277=x\\0.03=x[/tex]

80.6 square foot roll

[tex]\frac{1.89}{80.6}=\frac{x}{1} \\1.89=80.6x\\0.0234=x\\0.02=x[/tex]

Thus, per square foot, the 80.6 square foot roll is less expensive than the 53.7 square foot roll

The value of x in the triangular pyramid is 8 units.

The volume of the pyramid is given as 240 units cube. Therefore, let's find the value of x in the pyramid.

volume of the pyramid = 1 / 3 ×base area × height

Therefore,

base area = 1 / 2 bh

base area = 1 / 2 × 12 × x

base area = 6x

Therefore,

volume of the pyramid =  1 / 3 × 6x × 15

240 = 30x

divide both sides by 30

x = 240 / 30

x = 8 units

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The total change in All - Plus stock, given the change in one day and the dip the next day, would be - $ 3.125.

In the one day shown on the table, the price of All - Plus stock dropped by $ 2.50 dollars. The very next day, the price of the stock still dropped but this time by 1 / 4 of the fall in the first day so the fall was ;

= 1 / 4 x 2. 50

= $ 0. 625

This means that the total change in price can be found to be :

= Change in price first day + change next day

= 0. 625 + 2. 5

= $ 3. 125

This means prices of All - Plus stock changed by - $ 3.125.

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Work Shown:

r = 2 = radius

h = 3 = height

SA = surface area of the cylinder

SA = 2*pi*r^2 + 2*pi*r*h

SA = 2*pi*2^2 + 2*pi*2*3

SA = 8pi + 12pi

SA = 20pi   ....... exact surface area

SA = 20*3.1415926535898

SA = 62.831853071796

SA = 62.832 ....... approximate surface area

The corresponding height of similar rectangular prism m is 9 centimeter.

Given that, the volume of rectangular prism m is 17 cm³ and the volume of rectangular prism n is 136 cm³.

If two solids are similar, then the ratio of their volumes is equal to the cube of the ratio of their corresponding linear measures.

The height of n is 18 cm.

Here, m³/n³ = 17/136

m³/18³ = 17/136

m³/18³ = 17/136

(m/18)³ = 1/8

(m/18)³ = (1/2)³

m/18 = 1/2

m=9 cm

Therefore, the corresponding height of similar rectangular prism m is 9 centimeter.

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