Combine the like terms to create an equivalent expression:
-3x - 6+ (-1)
Stuck? Watch a video or use a hint.

Step-by-step explanation:

Area parallelogram = a×b×sin (x)

a, b = 6.7 ft and 5.6 ft

x = 152 degrees

so, we have

6.7×5.6×sin(152) = 37.52×sin(152) = 17.61457304... ft²

the rounded area is 17.6 ft².

Answer: -2n^3+13

Step-by-step explanation:

Use PEMDAS

P- ()

E _^

M *

D /

A +

S -

Answer:

x, 0 y, -3

Step-by-step explanation:

i couldn't bring a graph so this is just where to graph it

Perimeter, area, and circumference are important mathematical concepts that have numerous real-world applications.

How to apply?

For example, in construction and architecture, these concepts are used to measure and design buildings, rooms, and other structures. Knowledge of perimeter is important when determining how much material is needed for a fence or wall, while understanding area is crucial for calculating how much paint or flooring material is needed for a room.

Circumference is important for designing circular objects such as wheels, pipes, and round tables. In addition to construction and design, these concepts are also used in various fields such as engineering, science, and finance.

For instance, understanding area and circumference is important in calculating the surface area and volume of 3D objects in science, while in finance, perimeter and area can be used to calculate the cost of goods or real estate. Overall, the applications of perimeter, area, and circumference are numerous and essential in many aspects of our daily lives.

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Answer:

x > 2, x < -8

Interval notation:

( -infinity, -8) U (2, infinity)

Step-by-step explanation:

x(x+6) > 16

distribute x into x+6, multiply

x^2 + 6x > 16

bring 16 to left side, subtract

x^2 + 6x - 16 > 0

factors of -16 that add to +6 is -2 and +8

(x - 2)(x + 8) > 0

solve for x:

x < -8,  x > 2

Interval notation:

( -infinity, -8) U (2, infinity)

Answer:

70.59 feet

Step-by-step explanation:

There are a total of 14 parts when the wire is divided into a ratio of 1 to 13.

1. Divide 76 by 14

76 ÷ 14 = 5.43

2. Multiply the longer length of 13 parts

5.43 · 13 = 70.59

The longer length of the wire 70.59 feet

There are a total of 14 parts when the wire is divided into a ratio of 1 to 13.

1. Divide 76 by 14

76 ÷ 14 = 5.43

2. Multiply the longer length of 13 parts

5.43 · 13 = 70.59

In algebra, a decimal number can be defined as a range whose entire number part and the fractional element are separated by means of a decimal point. The dot in a decimal range is referred to as a decimal point. The digits following the decimal factor show a price smaller than one.

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Main Answer: The total surface area of cylinder B is approximately 476.7  square units.

Supporting Question and Answer:

How is the surface area of a cylinder calculated?

The surface area of a cylinder is the sum of the areas of its curved surface and two circular bases. It can be calculated using the formula:

A = 2πrh + 2π\(r^{2}\)

where "r" is the radius of the circular base, "h" is the height of the cylinder, and π (pi) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter, approximately equal to 3.14159.

The first term, 2πrh, represents the area of the curved surface of the cylinder, while the second term, 2π\(r^{2}\), represents the combined area of the top and bottom circular bases.

Body of the Solution: Let the height and radius of cylinder A be "h" and "r" respectively. Then, the height and radius of cylinder B are "2h" and "R" respectively, since cylinder B has twice the height of cylinder A but the same radius.

The total surface area of a cylinder is given by the formula:

Area = 2πrh + 2π\(r^{2}\)

For cylinder A, we know that the surface area is 180, so we can substitute the values and solve for "r" as follows:

180 = 2πrh + 2π\(r^{2}\)

90 = πrh + π\(r^{2}\)

We can rearrange this equation to solve for r:

r² + rh - 90/π=0

Using the quAdratic formula,we get:

r = (-h ± √((h)² + 4(90/π)))/2

r = -h/2 ± √(h² + 4(90/π))/2

Now we have an expression for r in terms of h . We can use this expression to find the radius of cylinder B, since we know that cylinder B has twice the height of cylinder A.

R = 2r= -h ± √(h² + 4(90/π))

We can use this expression to find the surface area of cylinder B:

Surface area of cylinder B = 2πR² + 2πR(2h)

Surface area of cylinder B= 2π( -h ± √(h² + 4(90/π)))² + 4πh( -h± √(h² + 4(90/π)))

We can use the value we found for 2h using the quadratic formula in the expression to get:

Surface area of cylinder B = 476.7 square units (rounded to one decimal place)

Therefore, the total surface area of cylinder B is approximately 476.7  square units.

Final Answer: Therefore, the total surface area of cylinder B is approximately 476.7  square units.

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The growth rate of the population, given the initial population and the population after 10 years is 12. 5 % every 10 years.

To find the percent change or growth rate of a quantity between two different values, you can use the formula:

Percent change = ( new value - old value ) / old value x 100%

The new value would be the population of the village after 10 years which is 450 people.

The old value is the initial population of the village which is 400

The growth rate of the population is:
= ( 450 - 400 ) / 400 x 100 %

= 12. 5 %

The growth rate for the village is therefore 12. 5 % every ten years.

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Answer:

104

Step-by-step explanation:

1st term + or - common difference (term -1)

common difference is +6

2 + 6 (18-1)

2 + 6 (17)

2 + 102

104

Answer: 107,000

Step-by-step explanation:

the exponent is a positive 5, so move the decimal point 5 places right.

if exponent is negative, go the other direction

Step-by-step explanation:

The cost of a cup of tea is t cents.

The cost of a cup of coffee is (t + 5) cents.

The total cost of 7 cups of tea and 11 cups of coffee is 2215 cents.

Therefore,

7t+11t+55=2215

18t=2160

t=120

x² + 3x - 2

(5)² + 3 × 5- 2

25 + 15 - 2

40 - 2

38...

The data in the question, which includes values based on one variable can be displayed graphically using a dot plot;

Part A; A dot plot

Part B; The dot plot for the specified data can be created by plotting the data points above corresponding values on an horizontal axis

A dot plot is a form of data visualization consisting of data point values plotted as dots on a graph with a horizontal x and a vertical y-axis.

The data can be presented as follows;

{91, 101, 102, 103, 106, 110, 114, 116, 117, 117, 118, 120, 121, 121, 125}

Part A; The data include some values which repeat themselves, such that a good graphical representation to display the data is a frequency based graphical representation, such as a dot plot.

Part B; To create a dot plot, the following steps are required;

The dot plot that results from the above steps will show the distribution of points the basketball team scored during the first 15 games of the season

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Answer:

so hard

Step-by-step explanation:

Answer:

\(r = 1.34\)

Step-by-step explanation:

Given

Solid = Cylinder + 2 hemisphere

\(Volume = 10cm^3\)

Required

Determine the radius (r) that minimizes the surface area

First, we need to determine the volume of the shape.

Volume of Cylinder (V1) is:

\(V_1 = \pi r^2h\)

Volume of 2 hemispheres (V2) is:

\(V_2 = \frac{2}{3}\pi r^3 +\frac{2}{3}\pi r^3\)

\(V_2 = \frac{4}{3}\pi r^3\)

Volume of the solid is:

\(V = V_1 + V_2\)

\(V = \pi r^2h + \frac{4}{3}\pi r^3\)

Substitute 10 for V

\(10 = \pi r^2h + \frac{4}{3}\pi r^3\)

Next, we make h the subject

\(\pi r^2h = 10 - \frac{4}{3}\pi r^3\)

Solve for h

\(h = \frac{10}{\pi r^2} - \frac{\frac{4}{3}\pi r^3 }{\pi r^2}\)

\(h = \frac{10}{\pi r^2} - \frac{4\pi r^3 }{3\pi r^2}\)

\(h = \frac{10}{\pi r^2} - \frac{4r }{3}\)

Next, we determine the surface area

Surface area (A1) of the cylinder:

Note that the cylinder is covered by the 2 hemisphere.

So, we only calculate the surface area of the curved surface.

i.e.

\(A_1 = 2\pi rh\)

Surface Area (A2) of 2 hemispheres is:

\(A_2 = 2\pi r^2+2\pi r^2\)

\(A_2 = 4\pi r^2\)

Surface Area (A) of solid is

\(A = A_1 + A_2\)

\(A = 2\pi rh + 4\pi r^2\)

Substitute \(h = \frac{10}{\pi r^2} - \frac{4r }{3}\)

\(A = 2\pi r(\frac{10}{\pi r^2} - \frac{4r }{3}) + 4\pi r^2\)

Open bracket

\(A = \frac{2\pi r*10}{\pi r^2} - \frac{2\pi r*4r }{3} + 4\pi r^2\)

\(A = \frac{2*10}{r} - \frac{2\pi r*4r }{3} + 4\pi r^2\)

\(A = \frac{20}{r} - \frac{8\pi r^2 }{3} + 4\pi r^2\)

\(A = \frac{20}{r} + \frac{-8\pi r^2 }{3} + 4\pi r^2\)

Take LCM

\(A = \frac{20}{r} + \frac{-8\pi r^2 + 12\pi r^2}{3}\)

\(A = \frac{20}{r} + \frac{4\pi r^2}{3}\)

Differentiate w.r.t r

\(A' = -\frac{20}{r^2} + \frac{8\pi r}{3}\)

Equate A' to 0

\(-\frac{20}{r^2} + \frac{8\pi r}{3} = 0\)

Solve for r

\(\frac{8\pi r}{3} = \frac{20}{r^2}\)

Cross Multiply

\(8\pi r * r^2 = 20 * 3\)

\(8\pi r^3 = 60\)

Divide both sides by \(8\pi\)

\(r^3 = \frac{60}{8\pi}\)

\(r^3 = \frac{15}{2\pi}\)

Take \(\pi = 22/7\)

\(r^3 = \frac{15}{2 * 22/7}\)

\(r^3 = \frac{15}{44/7}\)

\(r^3 = \frac{15*7}{44}\)

\(r^3 = \frac{105}{44}\)

Take cube roots of both sides

\(r = \sqrt[3]{\frac{105}{44}}\)

\(r = \sqrt[3]{2.38636363636}\)

\(r = 1.33632535155\)

\(r = 1.34\) (approximated)

Hence, the radius is 1.34cm

The radius of the cylinder that produces the minimum surface area is 1.34cm and this can be determined by using the formula area and volume of cylinder and hemisphere.

Given :

The volume of a cylinder is given by:

\(\rm V = \pi r^2 h\)

The total volume of the two hemispheres is given by:

\(\rm V' = 2\times \dfrac{2}{3}\pi r^3\)

\(\rm V' = \dfrac{4}{3}\pi r^3\)

Now, the total volume of the solid is given by:

\(\rm V_T = \pi r^2 h+\dfrac{4}{3}\pi r^3\)

Now, substitute the value of the total volume in the above expression and then solve for h.

\(\rm 10 = \pi r^2 h+\dfrac{4}{3}\pi r^3\)

\(\rm h = \dfrac{10}{\pi r^2}-\dfrac{4r}{3}\)

Now, the surface area of the curved surface is given by:

\(\rm A = 2\pi r h\)

Now, the surface area of the two hemispheres is given by:

\(\rm A'=2\times (2\pi r^2)\)

\(\rm A'=4\pi r^2\)

Now, the total area is given by:

\(\rm A_T = 2\pi rh+4\pi r^2\)

Now, substitute the value of 'h' in the above expression.

\(\rm A_T = 2\pi r\left(\dfrac{10}{\pi r^2}-\dfrac{4r}{3}\right)+4\pi r^2\)

Simplify the above expression.

\(\rm A_T = \dfrac{20}{r} + \dfrac{4\pi r^2}{3}\)

Now, differentiate the total area with respect to 'r'.

\(\rm \dfrac{dA_T}{dr} = -\dfrac{20}{r^2} + \dfrac{8\pi r}{3}\)

Now, equate the above expression to zero.

\(\rm 0= -\dfrac{20}{r^2} + \dfrac{8\pi r}{3}\)

Simplify the above expression in order to determine the value of 'r'.

\(8\pi r^3=60\)

r = 1.34 cm

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Answer:

Shorter than

Step-by-step explanation:

If Dave's height is above the median, it means that Dave's height is greater than the middle value of the heights of all the individuals being considered. In other words, Dave's height is higher than or equal to the height of the person who is exactly in the middle when all the heights are arranged in order from smallest to largest.

Answer:

Step-by-step explanation:

Answer:

the last one

is/of = x/100

12/20 = x/100

20x = 1200

x = 60% students would rather ride a bike

Step-by-step explanation:

The last pie graph best represents the given scenario. The correct option is D.

A circular statistical visual with slices illustrating numerical proportion is called a pie chart. Each slice's arc length in a pie chart corresponds to the quantity it represents.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

It is given that twelve out of twenty students say they would rather ride a bike than walk to school. The correct fraction represented on a pie graph will be calculated as below:

12/20 = x/100

20x = 1200

x = 60%

Therefore, the last pie graph best represents the given scenario. The correct option is D.

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y = x - 4 is  the equation of the line in slope-intercept form.

How do you interpret a slope-intercept form?

The data provided by that form can be used to graph a linear equation in slope-intercept form. As an illustration, the equation y=2x+3 indicates that the line's slope is 2 and that its y-intercept is located at (0,3). This reveals the single point at which the line passes as well as the direction in which we should draw the full line after that.

Point from graph = (2, -2 )

                slope (m) = y/x

                                = -2/2

                                = 1

slope-intercept form ⇒ y = mx + c    

                                        -2 = 1 * 2 + c

                                          - 2 = 2 + c

                                               c = -4

 slope-intercept form ⇒ y = x - 4

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Therefore, according to the given information, The formulas to find the area of a circle are\(\pi r^2 and (d/2)^2\pi or r^2\pi\).

The area of a circle is given by the formula A = πr², where r is the radius of the circle.

The area of a circle can be found using either of the following formulas:

\(\pi r^2\), where π (pi) is a mathematical constant approximately equal to 3.14159 and r is the radius of the circle.

\(A = (d/2)^2π,\) where d is the diameter of the circle. This formula can also be written as \($A = r^2\pi$\), where r is the radius of the circle and A is the area.

Both formulas are equivalent and can be used interchangeably, depending on the given information about the circle.

Therefore, according to the given information, The formulas to find the area of a circle are\(\pi r^2 and (d/2)^2\pi or r^2\pi\).

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Answer: el enunciado cinco veces la diferencia de un numero y 3 es 17

Step-by-step explanation:

Answer:

ATQ, 5( x -3 ) = 17

5 x - 15 = 17

5x = 17 + 15

x = 32 /5

x = 6.4 ,

Answer:

BC = 4

Step-by-step explanation:

The diagram shows a circle with radius AE and chord BD.

Assuming that the radius bisects the chord, then AE is perpendicular to BD. So the measure of angle ACB is 90°.

This means that triangle ACB is a right triangle, with legs AC and BC, and hypotenuse AB.

The length of the radius is:

\(AE = 3 + 2 = 5\)

As AB is also the radius, AB = 5.

To find the length of BC, use Pythagoras Theorem:

\(AC^2+BC^2=AB^2\)

    \(3^2+BC^2=5^2\)

      \(9+BC^2=25\)

\(9+BC^2-9=25-9\)

           \(BC^2=16\)

        \(\sqrt{BC^2}=\sqrt{16}\)

            \(BC=4\)

Therefore, the length of line segment BC is 4.

Answer:

2. The amount of soup in a can

3. The amount of chips in a bag of chips

5. The amount of chocolate that makes up a chocolate bar.

Step-by-step explanation:

Volume is the amount that a substance or object occupies, or that is enclosed within a container, so 1 and 4 wouldn't make sense since 1 is a shadow that doesn't take up anything three dimensional, and same goes with 4.

Answer:

the answer is 0

Step-by-step explanation:

6 (4) -2 (3)(4)

24-24=0

Answer: Total expenses if 3 widgets are produced is $11,018.00

Step-by-step explanation: The variable cost per unit is given by the coefficient of q in the expense function. In this case, the variable cost is $6.00 per widget. To find the variable costs to produce 2 widgets, we simply multiply the variable cost per unit by the number of units produced: Variable costs for 2 widgets = 2 x $6.00 = $12.00 Therefore, the variable costs to produce 2 widgets is $12.00. To find the variable costs to produce q widgets, we simply multiply the variable cost per unit by the number of units produced: Variable costs for q widgets = q x $6.00 = $6q Therefore, the variable costs to produce q widgets is $6q. To find the total expenses if 3 widgets are produced, we can use the expense function and substitute q = 3:E = 6.00 q + 11,000

E = 6.00 (3) + 11,000

E = 18.00 + 11,000

E = 11,018.00 Therefore, the total expenses if 3 widgets are produced is $11,018.00.

Answer:  Ryan should sell his CDs for $13 to maximize his revenue.

Step-by-step explanation:

To find the price at which Ryan should sell his CDs to maximize his revenue, we need to use the information provided about the relationship between price and sales, and the formula for revenue (price x quantity sold).

Step 1: Identify the relationship between price and sales. We know that a $1 increase in the price of a CD leads to a drop of 5 CDs per week in sales.

Step 2: Create an equation that relates price, quantity sold, and revenue. Let P be the price of a CD, Q be the quantity sold, and R be the revenue. Then, we have R = P x Q

Step 3: Create a table that shows the relationship between price, quantity sold, and revenue.

Price Quantity Sold         Revenue

10       80                            800

11       75                              825

12      70                                     840

13     65                                        845

14     60                                         840

15     55                                        825

16     50                                   800

17     45                                  785

18     40                                720

19     35                                      665

20     30                                              600

Step 4: Identify the price that maximizes revenue. From the table we can see that the revenue is maximum at $13 which is 845 and this is the price at which Ryan should sell his CDs to maximize his revenue.

Therefore, Ryan should sell his CDs for $13 to maximize his revenue.

Answer:

c

Step-by-step explanation: