find the area of the region that lies inside both curves. r^2 = 50 sin(2θ), r = 5

Answer:

30) 0.0,000,115

31) 0.00,000,000,022

32) 43,000,000,000

Step-by-step explanation:

30

1.15 x [tex]10^{-5}[/tex]  The negative exponent is telling us that the number in standards form is smaller than 1.15.  To write in standard form we move the decimal 5 places to the left.

0.0,000,115

31

2.2 x [tex]10^{-10}[/tex] This is like question 30, but we will move the decimal 10 places to the left this time.

0.00,000,000,022

32

4.3 x [tex]10^{10}[/tex]  the exponent is positive this time.  That means in standard from the number is much larger than 4.3.  Move the decimal point 10 places to the right.  If you do not see a decimal point, it means that it is at the end of the number.

43,000,000,000

A function f such that f '(x) = 3x^3 and the line 81x + y = 0 is tangent to the graph of f is f(x) = 3x^4/4 + 729/4.

In the given question, we have to find a function f such that f'(x) = 3x^3 and the line 81x + y = 0 is tangent to the graph of f.

The given function is f'(x) = 3x^3.

No integrating on both side,

f(x) = [tex]\int3x^3dx[/tex] + C

f(x) = 3x^4/4 + C

As given, the line 81x + y = 0 is tangent to the graph of f.

So, slope at point of tangent; f'(x) = -81

So, 3x^3 = -81

Divide by 3 on both side, we get

x^3 = -27

Taking cube root on both side, we get

x = -3

So putting the value of x in 81x + y = 0, we get

y = 243

Thus, f(x) passes through (-3, 243).

So, 243 = 3/4(81) + C

Multiply by 4 on both side, we get

972 = 243 + 4C

Subtract 243 on both side, we get

4C = 729

Divide by 4 on both side, we get

C = 729/4

So, f(x) = 3x^4/4 + 729/4

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The constant of proportionality for the data in the table is 65. This can be determined by dividing the number of trees planted by the number of weeks for each data point in the table. For example, for the first data point where 2 weeks have passed, 130 trees have been planted, which means the constant of proportionality is 65 (130 / 2 = 65). This value is the same for all of the data points in the table, which means it is the constant of proportionality for the data.

Answer: 96

Step-by-step explanation: This is how to solve:

120 * 4

= 480

3 + 2 = 5

480 / 5

= 96

First, you need to multiply the boxes bought by the total amount inside the box. (120 * 4)

The, we need to find how many raisins she uses IN TOTAL for each gingerbread man. So, we need to add 3 + 2

This equals 5

So, 120 * 4 = 480

So, in total, she buys 480 raisins. So, to find how much gingerbread she can make, we need to divide 480 by 5. This would get you 96. I hope this helps ;)

A graph [tex]\frac{1}{A_{t}}[/tex] and time yields a straight line for a second order reaction. The positive slope of the straight line is rate constant k for second order.

For a second order reaction A→B.

The integrated rate law is

-d[n]/dt = k[A]^{r}

where, k = rate constant of second order reaction and

[A]^{r} = concentration of [A]

-[tex]\int^{A_{t}}_{A_{0}}\frac{d[A]}{[A]^{r}} = k\int^{t}_{t_{0}}dt[/tex]

where, [tex]A_{t}[/tex] = concentration of A at time t

[tex]A_{0}[/tex] = concentration of A at time t=0

[tex]\frac{1}{A_{t}}-\frac{1}{A_{0}}=kt[/tex]

Adding [tex]\frac{1}{A_{0}}[/tex]on both side, we get

[tex]\frac{1}{A_{t}}=kt+\frac{1}{A_{0}}[/tex]....................(1)

On comparing the equation 1 by the equation y = mx+c, we get that the plot of [tex]\frac{1}{A_{t}}[/tex] and plot of time t will be in the straight line with the positive slope k.

The plot is given below:

Hence, a graph [tex]\frac{1}{A_{t}}[/tex] and time yields a straight line for a second order reaction. The positive slope of the straight line is rate constant k for second order.

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The complete question is given below:

Answer:

B / 2; <3 is congruent to <6

Step-by-step explanation:

To find a congruent angle you must find what can fit inside the giving number the best. If we compare all of the answer is wouldn't make sense, since 7 is greater than 6 it would be wrong. So, A is Incorrect.

C is about 3 and 7. C would fit but 7 wouldn't. So, C is incorrect.

D has both 2 and 3 but also have 4 and 7 which wouldn't match. So, D is incorrect.

( THIS IS WHAT I THINK IS IT)

Answer:

B

Step-by-step explanation:

When a roof has a pitch of 5 : 12 and the roof is 175'' horizontally the height of the roof from the lowest point to the highest point is solved to be 73''

The idea of the slope is represented in the form 5: 12 when calculating the height of the roof.

This indicates that there is a 5 increase for every 12 units.

The rise is equal to 5, and the run is 12.

The vertical is the ascent, and the run is the horizontal.

It is possible to compare using the provided ratio as follows.

Let x represent the rise so that

x / 175" = rise / run = 5 / 12

x / 175" = 5 / 12

cross multiplying

175 * 5 = 12x

12x = 875

x = 875 /12

x = 72.92 ''

The height of the roof, measured from its lowest to its highest point, is calculated to be 73 inches.

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Answer:

b = -144

Step-by-step explanation:

b/24 = -6

Multiple 24 on both sides since it's being divided.

b = -144

Answer:

[tex] \sf \: b = - 144[/tex]

Step-by-step explanation:

Now we have to,

→ find the required value of b.

The equation is,

→ b/24 = -6

Then the value of b will be,

→ b/24 = -6

→ b = (-6) × 24

→ [ b = -144 ]

Hence, the value of b is -144.

An arithmetic sequence is a sequence of numbers in which each term after the first is obtained by adding a fixed number, called the common difference, to the previous term. For example, the sequence 15, 12, 9, 6, … is an arithmetic sequence because each term is obtained by subtracting 3 from the previous term, which is the common difference. On the other hand, the sequence 15, 30, 60, 120, … is not an arithmetic sequence because the difference between each consecutive pair of terms is not constant. The same is true for the sequences 1, 4, 9, 16, … and 1, 8, 27, 64, …. Therefore, the only arithmetic sequence among the given options is 15, 12, 9, 6, ….

The exponential function in the form y = ab^x is y = 18(7)^x

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

Points: (0, 18) and (3,6174).

The above can be represented as

(x, y) = (0, 18) and (3,6174).

An exponential function is represented as

y = ab^x

Where

a = y when x = 0

This means that

a = 18

So, we have

y = 18b^x

At (3,6174), we have

6174 = 18b^3

So, we have

343 = b^3

Take the cube root of both sides

b = 7

This means that

y = 18(7)^x

Hence, the function is y = 18(7)^x

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Based on the above, Mr. Smith runs approximately 985.5 miles in one year

To calculate the number of miles Mr. Smith runs in one year, we can multiply the distance he runs each day by the number of days in a year.

Number of miles Mr. Smith runs in one day: 2.7 miles

Number of days in a year: 365 (assuming a non-leap year)

S, one  can calculate the total distance he runs in one year:

Total miles in one year = Distance per day * Number of days in a year

= 2.7 miles x  365 days

= 985.5 miles

Therefore, Mr. Smith runs about 985.5 miles in one year.

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Answer:

1,100

Step-by-step explanation:

1000 x 0.1 = 100

1000 + 100 = 1,100

Answer:

Step-by-step explanation: y+9=-3(x-4)......given equation

This equation can be expanded further and simplified

y+9=-3x+12

We want to put the equation into the form y=mx+b so we can read its characteristics

To do this we need to get y on its own. We must take 9 from both sides

y+9-9=-3x-9+12

y=-3x+3

The equation has a gradient or slope or m =-3 and it cuts the y-axis at +3 or is the yintercept

Answer:

3.1 mm

Step-by-step explanation:

as 1mmx3.14=3.14mm

And then correct it to 1 decimal place =3.1

Answer:

A. 1 cm and 5 cm

Step-by-step explanation:

Let me know if my work makes sense!

A) First we need to subtract the tax, the correct option is D.

B) by dividing the total cost without the tax by the number of people, we wiill see that each ticket costs $6, the correct option is C.

We want to find the total cost of each ticket not including the tax, then the first thing that we need to doo is take the total cost ($256) and subtract the $10 of the tax, we will ge:

$256 - $10 = $246

Then the correct option is D

"Subtract $10 from $256 to find the total cost of the tickets without the tax."

Part B:

Now we can divide that amount by the number of people so we get how much each ticket costs:

19 + 22 = 41

We will get:

$246/41 = $6

Then the correct option is C.

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The fraction or ratio for the bracelet aren't equivalent.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

On the other hand, a fraction appears in the numerator or the denominator of a complex fraction.

Here Marcia made 10 bracletes for 5 friends. This will be:

= 10/5

= 2:1

Jen made 1 braclets for 4 friends. This will be:

= 1/4.

= 1:4

The fraction or ratio aren't equivalent.

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To answer the question, Miae needs 3/8 cup of sugar for 1/2 of a batch, it is important to understand the concept of fractions. miae is baking .the recipe uses 3/4 cup sugar.Miae needs 3/8 cup of sugar for 1/2 of a batch.

To answer the question, Miae needs 3/8 cup of sugar for 1/2 of a batch, it is important to understand the concept of fractions. A fraction is a part of a whole, it is represented by a numerator and denominator, the numerator represents the number of parts and the denominator represents the total number of parts. In this question, the recipe calls for 3/4 cup of sugar for the entire batch, so to get 1/2 of the batch, Miae needs to divide the fraction by 2. To do this, we can either divide the numerator and denominator by 2, or multiply the fraction by 1/2. In this case, 3/4 multiplied by 1/2 is 3/8, so Miae needs 3/8 cup of sugar for 1/2 of a batch.

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the work done is equal to the force applied (500 lb) multiplied by the distance (100 ft), resulting in 500 ft-lb of work done.

A force applied across a distance is what is referred to as work.

In this problem,

the force applied is the weight of the cable (5 lb/ft) multiplied by the length of the cable (100 ft).

Therefore, the work done is equal to the force applied (500 lb) multiplied by the distance (100 ft), resulting in 500 ft-lb of work done.Work is a force applied across a distance, and it is measured in a unit of energy called foot-pounds. In this problem, the force applied is the weight of the cable (5 lb/ft) multiplied by the length of the cable (100 ft). Therefore, the work done is equal to the force applied (500 lb) multiplied by the distance (100 ft), resulting in 500 ft-lb of work done. This means that 500 ft-lb of energy must be expended in order to move the cable 100 ft. This energy can be provided by a variety of sources, such as human labor, a motor, or some other mechanism.

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The measurement of angles △XYZ are ∠X = 59°, ∠Y = 89°, and ∠Z = 32°.

The measurement of angles △LMN are ∠L = 59°, ∠M = 89°, and ∠N = 32°.

What is angle?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

Given that, △XYZ and △LMN are similar triangle.

Since the triangles are similar, thus the measurement of triangles are similar.

Therefore,

∠X = ∠L, ∠Y = ∠M, ∠Z = ∠N.

∠Y = ∠M = 89° and ∠Z = ∠N = 32°.

The sum of all interior angles of triangle is 180°.

∠X + ∠Y + ∠Z = 180°

∠X + 89° + 32° = 180°

∠X + 121° = 180°

Subtract 121° from both sides:

∠X  = 59°

∠X = ∠L = 59°.

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Answer: See attached for the graph.

Step-by-step explanation:

     To find the answer to this question, we will isolate the variable x.

   Given:

|x| + 3 > 3

   Subtract 3 from both sides of the equation:

|x| > 0

  Aboslute value:

x > 0, x < 0

   This means the graph will be greater than or less than 0.

Answer:5103

Step-by-step explanation:We only care about 7xy6, cause it's the only term involving x In your example y = −3, thus 7(−3)6x = 7 ⋅ 729x = 5103x The coefficient of x is 5103

The polygon for the given data will be a square. The correct option is E.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other. The meaning of congruency is that the two shapes are similar as well as equal in size.

A square is a quadrilateral having all the sides equal and all the angles congruent to each other. The value of all the angles is 90 degrees and the sum of the angles of the square is 360 degrees.

The given data is that all the sides are congruent and all the angles are congruent so the given figure is square.

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a) The volume of the gas is 0.923 x [tex]10^{-6}[/tex] m³.

b) The pressure of the gas is 0.532 x [tex]10^7[/tex] Pascals.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

3 = 4k is an equation.

We have,

Volume of a gas (V) ∝ 1/ Pressure of a gas (P)

This can be written as,

Volume of a gas = K / Pressure of a gas

K = VP

Now,

P =1.8 x [tex]10^6[/tex] Pascals

V = 2.1 x [tex]10^{-8}[/tex] m³

K = VP = 1.8 x 2.1 x [tex]10^{-2}[/tex]

k = 3.78 x [tex]10^{-2}[/tex] pascal m³

Now,

P = 4.1 x [tex]10^4[/tex] Pascals

V = K/P =  3.78 x [tex]10^{-2}[/tex] Pascal m³ / 4.1 x [tex]10^4[/tex] Pascals

V = 0.923 x [tex]10^{-6}[/tex] m³

Now,

V = 7.1 x [tex]10^{-9}[/tex] m³

P = k/V =  3.78 x [tex]10^{-2}[/tex] Pascal m³ / 7.1 x [tex]10^{-9}[/tex] m³

P = 0.532 x [tex]10^7[/tex] Pascals

Thus,

The volume is 0.923 x [tex]10^{-6}[/tex] m³.

The pressure is 0.532 x [tex]10^7[/tex] Pascals.

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The set of the values of the side lengths of an isosceles triangle that has a hypotenuse that is 8 units long is: C. 4√2, 4√2, and 8.

An isosceles triangle is a type of triangle that has two sides that are of the same length, while the third side has a different length.

The hypotenuse is found in a triangle that has a right angle. This means the triangle is a right triangle, and therefore, according to the Pythagorean theorem, the square of the length of the hypotenuse is equal to the sum of the squares of the other legs of the triangle.

Considering the definition given above, it means the right triangle we are looking for must be a right triangle is isosceles, which hast two equal sides and an hypotenuse that is 8 units long.

The values of the set of lengths, 2, 4, and 8 cannot be the isosceles triangle because they have three different side lengths.

8,8, and 16 do not conform to the Pythagorean Theorem because:

16² ≠ 8² + 8²

4√2, 4√2, and 8 conform to the Pythagorean Theorem because:

8² = (4√2)² + (4√2)²

64 = 64

Therefore, the values of side lengths are: C. 4√2, 4√2, and 8.

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Answer:

4a)   [tex]P=2L+2W[/tex]

4b)  

       [tex]42=2L+2W\\L=2W+3[/tex]

4c)  

     [tex]L=15\\W=6[/tex]

Step-by-step explanation:

Note:

[tex]P=[/tex] Perimeter

[tex]L=[/tex] Length

[tex]W=[/tex] Width

The perimeter of a rectangle is the sum of all its sides.

We can say

[tex]P=L+L+W+W[/tex]

Which simplifies to

[tex]P=2L+2W[/tex]

This is the equation to find the perimeter of a rectangle.

We are given the perimeter which is 42.

We are also given that the length is the sum of twice its width and 3.

So we can write

[tex]42=2L+2W\\L=2W+3[/tex]

Lets solve using substitution.

Substitute [tex]L=2W+3[/tex] into the first equation.

[tex]42=2W+2(2W+3)[/tex]

Expand the right side of the equation then simplify.

[tex]42=2W+4W+6\\42=6W+6[/tex]

Subtract 6 from both sides.

[tex]36=6W[/tex]

Divide both sides by 6 to isolate [tex]W[/tex].

[tex]W=6[/tex]

Perform a back substitution.                                                                           Substitute [tex]W=6[/tex] into the second equation, [tex]L=2W+3[/tex]

[tex]L=(2*6)+3\\L=12+3\\L=15[/tex]

A rating/review would be much appreciated! Have a good Christmas!

Using the normal distribution, the middle 50% would be expected to be in the range of 250 to 270 days.

Using the central limit theorem, for the samples of 36, the middle 50% would be expected to be in the range of 258 to 262 days.

A sort of continuous probability distribution for a real-valued random variable is the normal distribution or the Gaussian distribution.

Normal Distribution of Probabilities

The z-score formula, which for a measure X, in a set with mean and standard deviation, is given by: can be used to address problems with normal distributions.

Z = (X - μ)/σ

The z-score calculates the measure's standard deviation from the mean.

A p-value, or percentile of X, is assigned to each z-score.

Mean (μ) = 260.

Standard deviation (σ)= 15 .

The normal distribution is symmetric, which means that the middle 50% is between the 25th percentile and the 75th percentile.

The 25th percentile is X when Z has a p-value of 0.25, so X when Z = -0.675.

The 75th percentile is X when Z has a p-value of 0.75, so X when Z = 0.675.

Lower bound:

Z = (X - μ)/σ

⇒ -0.675 = (X - 260)/15

⇒ X - 260 = -0.675*15

⇒ X - 260 = -10.125

⇒ X = 260 - 10.125

⇒ X ≈ 250

Upper bound:

Z = (X - μ)/σ

⇒ 0.675 = (X - 260)/15

⇒ X - 260 = 0.675*15

⇒ X - 260 = 10.125

⇒ X = 260 + 10.125

⇒ X ≈ 270

The middle 50% of pregnancies would be in the range of 250 to 270 days.

For sample of 36: By the Central Limit Theorem, the standard deviation of the sampling distribution of sample means of size n is given by .

Sample of 36, thus n=36, s=15/√36

⇒ s=15/6

⇒ s=2.5

Lower bound:

Z = (X - μ)/s

⇒ -0.675 = (X - 260)/2.5

⇒ X - 260 = -0.675*2.5

⇒ X - 260 = -1.69

⇒ X = 260 - 1.69

⇒ X ≈ 258

Upper bound:

Z = (X - μ)/s

⇒ 0.675 = (X - 260)/2.5

⇒ X - 260 = 0.675*2.5

⇒ X - 260 = 1.69

⇒ X = 260 + 1.69

⇒ X ≈ 262

The middle 50% of pregnancies would be in the range of 258 to 262 days.

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With 450 kids and chaperone there are 451 passengers to be transported, Using simple unitary method, The answer is 6 buses.

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unitary method's formula is to identify the value of a single unit, then multiply that value by the number of units to obtain the required value.

The arithmetic operator is used to carry out mathematical operations on the provided operands, including addition, subtraction, multiplication, division, and modulus.

total members to be transported = 451

each bus hold = 80

Number of bus needed = 451/80 = 5.63

So, We need 6 buses in total.

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A plot of all the ordered pairs for the values in the domain is shown in the graph attached below.

In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain is the set of all possible input values (x-values) to a function and the domain of a graph consist of all the input numerical values which are shown on the x-axis.

Based on the values given for the domain of this function, the ordered pairs would be calculated as follows:

When x = -8, we have;

y = 1/2(-8) + 1

y = -3

Ordered pair = (-8, -3)

When x = -4, we have;

y = 1/2(-4) + 1

y = -1

Ordered pair = (-4, -1)

When x = 0, we have;

y = 1/2(0) + 1

y = 1

Ordered pair = (0, 1)

When x = 2, we have;

y = 1/2(2) + 1

y = 2

Ordered pair = (2, 2).

When x = 6, we have;

y = 1/2(6) + 1

y = 4

Ordered pair = (6, 4)

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