write a formula that expresses the first variable as a function of the second: 1.the area of a circle as a function of its diameter

Answer:

6. 4.5×10⁴

7. 4.2×10^-3

8. 9.5×10^9

9. 1.3×10^-3

10. 3×10²

Step-by-step explanation:

start counting just after the dot . hope it helps

Answer:

7. 4.2× 10. -3

8. 9.5× 10 9

9. 1.3× 10-3

10. 3.0×10 2

Answer:

Step-by-step explanation:

225+36 = 261

\(\sqrt{261}\)

The corresponding point on the unit circle for the angle θ = 5pi/3  is given by: (0,5, -0.866).

What is the unit circle?

Basically, the unit circle is a circle with a radius of 1. It is used in trigonometry to help define and understand angles and their associated trigonometric values. The unit circle is centered at the origin (0, 0) of the coordinate plane, and each point on the circle is defined by its distance from the origin and its angle from the positive x-axis.

What is area of circle ?

The area of circle can be defined as the product of pi and square of radius of a given circle.

In this problem, we have that θ = 5pi/3 , hence:

cos θ = 0.5

sin θ = -0.866

Thus the point is (0,5, -0.866).

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Answer:

i

Step-by-step explanation:

i

The surface area of the composite figure is 1,665.04 in².

The volume of composite figure is 1,079.66 in³.

The volume  and surface area of the composite figure is calculated by applying the following formula as shown below;

The surface area = area of cone + area of hemisphere

S.A = πr(r + l) + 3πr²

S.A = π x 10 (10 + 13)  +  3π(10²)

S.A = 1,665.04 in²

The volume of composite figure is calculated as follows;

V = ¹/₃πr²h  +  ²/₃πr²

The height of the cone is calculated;

h = √(13² - 10²)

h = 8.31 in

V = ¹/₃π(10)²(8.31)  +  ²/₃π(10)²

V = 870.22 + 209.44

V = 1,079.66 in³

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Answer:

x=-.5

Step-by-step explanation:

y=0.5x+3

2x+.5x+3=-2

2.5x+3=-2

      -3   -3

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

2.5x=-5

     x=-.5

Answer:

Part A

a. Could be a parallelogram but cannot be a rectangle

Part B

c. 100°

Step-by-step explanation:

Part A

The polygon constructed by Andrew = Four sided polygon having no right angles

From the given four sided polygon (quadrilateral) options, the options which can have no right angles are the parallelogram, and rhombus

The rectangle, and square both have 4 right angles

Therefore, the polygon can be either a parallelogram or a rhombus, but cannot be either a rectangle or square

The correct option is therefore, 'His polygon could be a parallelogram but cannot be a rectangle'

Part B

The given parameters of the rhombus EFGH are;

Angle E = 3·x + 5, angle H = 4·x

The characteristics of a rhombus are;

The sum of the interior angles of a rhombus = 360°

The opposite angles of a rhombus are equal

The sum of the adjacent angles = 180° (The adjacent angles are supplementary)

Therefore, in the rhombus EFGH, we have;

Angle E, and angle H are supplementary angles

∴ Angle E + angle H = 180°

Substituting the values of angle E and angle H gives;

3·x + 5 + 4·x = 180°

7·x = 180° - 5 = 175°

x = 175°/7 = 25°

Angle H = 4·x

∴ Angle H = 4 × 25° = 100°

Angle H = 100°

Angle F = angle H = 100°

Therefore, angle F = 100°

The cost of each apple is equal to $0.23.

An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=8x+3. Where:

m= the slope.

b= the constant term that represents the y-intercept.

For the given example: m=8 and b=3.

The question gives:

You should convert the data into an equation:

15A+2.75=6.20

15A=6.20-2.75

15A=3.45

A=3.45/15

A=0.23

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the equation of the least squares regression line is y = 0.2x + 13.1. This equation represents the line that provides the best fit to the given data points.

The least squares regression line represents the line that best fits a given set of data points. It is determined by finding the slope and intercept of the line.

Given:

x-bar = 15 (mean of x values)

sx = 2 (standard deviation of x values)

y-bar = 17.1 (mean of y values)

sy = 3 (standard deviation of y values)

r = 0.2 (correlation coefficient)

The slope of the regression line, denoted as b, can be calculated using the formula:  b = r × (sy / sx)

Substituting the given values: b = 0.2 * (3 / 2) = 0.3

The intercept of the regression line, denoted as a, can be calculated using the formula: a = y-bar - b × x-bar

Substituting the given values: a = 17.1 - 0.3 × 15 = 13.1

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Answer:

y = -1x + 2

Step-by-step explanation:

Answer:

(2, 3 )

Step-by-step explanation:

- x + 3y = 7 → (1)

x - 4y = - 10 ( add 4y to both sides )

x = 4y - 10 → (2)

Substitute x = 4y - 10 into (1)

- (4y - 10) + 3y = 7 ← distribute parenthesis by - 1

- 4y + 10 + 3y = 7

- y + 10 = 7 ( subtract 10 from both sides )

- y = - 3 ( multiply both sides by - 1 )

y = 3

Substitute y = 3 into (2)

x = 4(3) - 10 = 12 - 10 = 2

solution is (2, 3 )

Answer:

8 Units long

The independent variable is the cause. Its value is independent of other variables in your study. The dependent variable is the effect. Its value depends on changes in the independent variable.

The independent variable, as indicated in the name is not influenced by other variables but can predetermine its own self.

So, the independent variable is the water in the 200 gallon aquarium

Now, the dependent variable is the tested variable and is depends on the independent variable, which is the time it takes to drain the 200 gallon aquarium.

Hence,  independent variable is volume of water in the aquarium and dependent variable is time it will take to drain the aquarium.

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Refer to the attachment

Answer:

\({ \underline{ \mathfrak{ \: asnwer : }}}\)

Richard's investment = David's investment

• From compound interest formula:

\({ \boxed{ \bf{investment = p(1 + \frac{r}{100}) {}^{n} }}}\)

Therefore:

\({ \rm{10000(1 + \frac{x}{100}) {}^{7} = 10000(1 + \frac{2}{100}) { }^{7} }} \\ \\ { \rm{1 + \frac{x}{100} = 1 + \frac{2}{100} }} \\ \\ { \rm{x = \frac{2 \times 100}{100} }} \\ \\ { \boxed{ \rm{ \: x = 2 \: }}}\)

The completed table shows the products of each term. we get

       |  2z  |  -4

____________________

22²       | 44z² |

__________|______|______

3zy       | 6zy  | -12z

__________|______|______

-2y²      | -4y² | 8y²

To use the box method for multiplying the two expressions, let's create a table with the terms of each expression:

         |  2z  |  -4

____________________

22²       |

__________|______|______

3zy       |

__________|______|______

-2y²      |

Now, we will multiply each term from the first expression with each term from the second expression and fill in the table:

         |  2z  |  -4

____________________

22²       | 44z² |

__________|______|______

3zy       | 6zy  | -12z

__________|______|______

-2y²      | -4y² | 8y²

The completed table shows the products of each term.

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Answer:

A,C and D

Step-by-step explanation:

This indicates that approximately 47.7% of the sampled subjects responded definitely or probably not beneficial to family planning.

From the given data, we can analyze the proportions of respondents who considered family planning beneficial and those who did not.

The proportion of respondents who responded definitely or probably beneficial is 651 out of 1245 sampled subjects. Therefore, the proportion can be calculated as:

Proportion = 651/1245 ≈ 0.523

This indicates that approximately 52.3% of the sampled subjects responded definitely or probably beneficial to family planning.

On the other hand, the proportion of respondents who responded definitely or probably not beneficial is 594 out of 1245 sampled subjects. The proportion can be calculated as:

Proportion = 594/1245 ≈ 0.477

This means that roughly 47.7% of the sampled participants indicated that family planning was either definitely advantageous or probably not beneficial.

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Step-by-step explanation:

When a = 6,

7(a + 2) = 7(a) + 7(2) = 7(6) + 7(2) = 7(6) + 14.

Answer:

7(6)+14

Step-by-step explanation:

7(6+2) = 7(6) + 7(2) = 7(6) + 14

Answer:

Its 16/81

Step-by-step explanation:

The information indicates that the correct answer is 9.76% annually.

The area of mathematics that deals with the characteristics of surrounding space, spatial interactions between distinct objects, and the shape of particular items.

It would take 19 years between 1996 and 2015 in all.

We are aware that the equation: gives a geometric mean of a collection of n positive numbers.

GM =  \(((x1)(x2)(x3).............)^{1/n}\)

This would provide us with the product of these values' nth roots.

Thus, the following would be the formula indicating rate of rise over time: -

GM =  \((value at the end of the period / value at the start of the period)^{1/n} -1\)

[value at the end of the period / value at the start of the period

Value at the conclusion of the time is equal to 241,364,256, hence the statement stands.

The initial value was 40,257,000.

n = 19

Using values, we obtain:

=\((241,364,256/40,257,000)^{1/19} -1\)

= (5.995)1/19 - 1

= 0.0976

= 9.76% per year

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Answer:

There is an infinite number of solutions.

All points on line 3x - 2y = 12 are solutions.

Step-by-step explanation:

3x - 2y = 12

6x - 4y = 24

Divide both sides of the second equation by 2:

3x - 2y = 12

Both equations are the same equation, so there is an infinite number of solutions. All points on line 3x - 2y = 12 are solutions.

Hey there! :)

Answer:

Infinite solutions.

Step-by-step explanation:

Solve this system of equations by subtracting the first equation from the second:

6x - 4y = 24

3x - 2y = 12

Multiply the bottom equation by 2 to make the terms with the y variable equivalent:

6x - 4y = 24

6x - 4y = 24

Subtract:

0x + 0y = 0

0 = 0

Therefore, there are infinite solutions to the system of equations.

The main idea is using the Pythagorean formula to find the length of line segment \(DB\).

Alr so you use the formula \(A^2 + B^2 = C^2\)

\(C^2\) is already given and is \(2\sqrt{5}\)

and \(A^2\) is \(3\sqrt{2}\)

So using algebraic rules you'll get \(B\) as:

\(\sqrt{2}\)

Now using the formula: \(\frac{1}{2} b * h\), you can find the area of tri ABD and CBD which would be \(3\) and \(1\) so add them up and you get \(4\)!

The pair of figures having same volume are:

a. The cylinder has a radius of 3 units and a height of 8 units ; The cone has a radius of 6 units and a height of 6 units.

b. The cone has a radius of 8 units and a height of 9 units ; The cylinder has a radius of 4 units and a height of 12 units.

c. The rectangular prism length is labeled 16 units, width of 6 units, and height of 6 units ; The rectangular prism length is labeled 8 units, width of 8 units, height of 9 units.

What is volume of a figure?

Volume is a unit of measurement for three-dimensional space. It is usually stated quantitatively in terms of a number of imperial or US-standard units as well as SI-derived units.

i. The cone has a radius of 4 units and a height of 12 units.

⇒ Volume = π\(r^{2} \frac{h}{3}\)

⇒ Volume = π\(4^{2} \frac{12}{3}\)

⇒ Volume = 64 π

⇒ Volume = 201 cubic units

ii. The rectangular prism has a length of 18 units, a width of 6 units, a height of 6 units.

⇒ Volume = length * width * height

⇒ Volume = 18 * 6 * 6

⇒ Volume = 648 cubic units

iii. The rectangular prism length is labeled 16 units, width of 6 units, and height of 6 units.

⇒ Volume = length * width * height

⇒ Volume = 16 * 6 * 6

⇒ Volume = 576 cubic units

iv. The cylinder has a radius of 3 units and a height of 8 units.

⇒ Volume = π\(r^{2}\)h

⇒ Volume = π\(3^{2}\) * 8

⇒ Volume = 72 π

⇒ Volume = 226 cubic units

v. The cone has a radius of 8 units and a height of 9 units.

⇒ Volume = π\(r^{2} \frac{h}{3}\)

⇒ Volume = π\(8^{2} \frac{9}{3}\)

⇒ Volume = 192 π

⇒ Volume = 603 cubic units

vi. The rectangular prism length is labeled 8 units, width of 8 units, height of 9 units.

⇒ Volume = length * width * height

⇒ Volume = 8 * 8 * 9

⇒ Volume = 576 cubic units

vii. The cylinder has a radius of 4 units and a height of 12 units.

⇒ Volume = π\(r^{2}\)h

⇒ Volume = π\(4^{2}\) * 12

⇒ Volume = 192 π

⇒ Volume = 603 cubic units

viii. The cone has a radius of 6 units and a height of 6 units.

⇒ Volume = π\(r^{2} \frac{h}{3}\)

⇒ Volume = π\(6^{2} \frac{6}{3}\)

⇒ Volume = 72 π

⇒ Volume = 226 cubic units

Hence, three pairs have the same volume.

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The missing figures have been attached below.

D) y = 2x + 8

Parallel lines are coplanar lines that never intersect.

Parallel Slopes

All parallel lines have the same relationship between their slopes. For 2 lines to be parallel, their slopes must be equal. The question tells us that the slope of the first line is 2. This means that only answer choices B and D are viable.

The slopes of answer choices A and C are perpendicular to the line given.

Testing the Answers

Both B and D could be parallel to the line given; however, we are also told that the line must pass through (-2, 4). To see which answer is correct, we can plug in the x and y-values and solve. If a line passes through a point, then the equation will be true when the values are plugged in.

Let's start with answer B.

Since this statement is not true, we know that y = 2x + 4 does not pass through the point (-2, 4).

Next, we need to test answer choice D.

This is true, so y = 2x + 8 must pass through the point (-2, 4). Since answer choice D has a parallel slope and passes through (-2, 4), it must be the correct answer.

Answer: (n^6 j^6)/(8h^5)

Step-by-step explanation:

Therefore:  n^6*j^6/8h^5

Based on the given information, the amount of capital this year (K1) could be something less than 25 (option c).

To determine the amount of capital this year based on the given information, we can use the investment and depreciation rates.

Let's denote the amount of capital this year as K1.

According to the information provided:

People invest 55% of income, but we don't have any information about income. Therefore, we cannot determine the exact investment amount.

10% of capital depreciates. Based on this, the capital at the beginning of this year (K1) can be calculated as follows:

K1 = K - 0.1K

= 0.9K

Since we know that the capital last year was equal to 25, we substitute K = 25 into the equation above:

K1 = 0.9 * 25

= 22.5

Therefore, based on the given information, the amount of capital this year (K1) could be something less than 25 (option c).

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Answer:

Erm

Step-by-step explanation:

Answer:

i think its B

Step-by-step explanation:

hope this helps

22 % probability of selecting 2 oranges from the fruits..

A probability is the number of desired outcomes divided by the number of total outcomes.

The probability of choosing 2 oranges will be calculated as:-

Initially, there are 8+11+5+12 = 36 fruits, of which 12 are oranges.

The total number of the fruits is 36 and we have to choose 2 oranges

Then

\(P=\dfrac{8}{36}=0.22=22\%\)

Therefore there is a 22 % probability of selecting 2 oranges from the fruits..

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Answer:

A. 0

Step-by-step explanation:

Slope tells you steepness or flatness of your line.

If you know two points on a line find slope by subtracting the y's and put that on top of a fraction. And subtract the x's and put that on the bottom of the fraction.

Subtract y's: 3 - 3

Put it on top: 0/...

Subtract x's: 5 - -4

same as 5+4

Put that on the bottom: 0/9

slope, usually called m, is 0/9, which is 0.

Notice if you graph these two points its a hOrizOntal line. HOrizOntal lines have zerO slope.