This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. A tank contains 15,000 L of brine with 22 kg of dissolved salt. Pure water enters the tank at a rate of 150 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. Exercise (a) How much salt is in the tank after t minutes? Click here to begin! Exercise (b) How much salt is in the tank after 10 minutes? Click here to begin! Need Help? Read It Talk to a Tutor

The percentage of 8th graders who send more than 50 texts is 56.15%

Here we want to find the percentage of eight grades who send more than 50 texts, and to get that we need to use the values in the table.

The formula for that percentage is:

P = 100%*(number that send more than 50 texts)/(total number)

On the table we can see that the total number of 8th gradesr is 130, and the number that send more than 50 messages is 73, then the percentage is:

P  = 100%*(73/130)

P = 56.15%

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Answer:

x>7

Step-by-step explanation:

The circle is open so seven is not included which eliminates the second and fourth choice.

x<7 means x is less than seven which is wrong.

x> means x is greater than seven.

Answer:

x > 7

Step-by-step explanation:

We see that the arrow is going to the right, signaling greater than.

We know that it is not greater than or equal to, since the dot is not shaded.

So, the answer is x > 7.

The probability of spotting 3 imperfections plates in 3 minutes is .3352.

The probability of spotting 3 imperfections plates in 3 minutes can be calculated using the binomial probability formula. This formula is used to calculate the probability of getting a certain number of successes in a certain number of trials (n), given a certain probability of success (p) for each trial.

In this case, the probability of success (p) is .15 and the number of trials (n) is 3. The formula for this is:

[tex]P(X = 3) = 3C3(.15)^3(1-.15)^(3-3)[/tex]

P(X = 3) = .3352

Therefore, the probability of spotting 3 imperfections plates in 3 minutes is .3352.

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The new coordinates would be

W' (12 , 6)

X'( 24 , 18 )

Z'(24 ,6 )

What exactly does coordinate geometry mean?

The term "coordinate geometry" refers to the study of geometry using coordinate points (or analytic geometry). Calculating distances between points, segmenting lines into m:n pieces, finding a line's midpoint, figuring out a triangle's area in the Cartesian plane, and other operations are all achievable with coordinate geometry.

Remember that the rule for a dilation by a factor of k about the origin is

 (x,y) = (kx, ky)

Identify the coordinates of the points W, X and Z. Then, apply a dilation by a factor of 3 about the origin to find W', X' and Z', the new coordinates after the dilation.

  w = (4,2)

   x = ( 8, 6 )

   z = ( 8,2)

Apply a dilation by a factor of 3:

  W(4,2) ⇒ W'(3 * 4, 3 * 2) = W' (12 , 6)

 X(8 ,6 ) ⇒ X'(3 * 8 , 3 * 6 ) = X' ( 24 , 18 )

 Z(8 , 2 ) ⇒ Z'(3*8 , 3 * 2) = Z'(24 ,6 )

Therefore, the new coordinates would be

W' (12 , 6)

X'( 24 , 18 )

Z'(24 ,6 )

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Answer: 0.48

Step-by-step explanation:

× 0.1 = ÷10

÷ 0.1 = ×10

× 0.01 = ÷100

÷ 0.01 = ×100

So, we do=

4.8 x 0.1 = 4.8 ÷ 10

= 0.48

So our answer is 0.48

The four points with y-coordinates half their x-coordinates are (0,0), (2,1), (4,2), and (6,3). These points do lie on a line, as they all satisfy the linear equation y = x/2.

To plot four points whose y-coordinates are half their x-coordinates, we can choose any four values of x and then compute the corresponding values of y using the equation y = x/2. For example

If x = 0, then y = 0/2 = 0, so the first point is (0,0).

If x = 2, then y = 2/2 = 1, so the second point is (2,1).

If x = 4, then y = 4/2 = 2, so the third point is (4,2).

If x = 6, then y = 6/2 = 3, so the fourth point is (6,3).

We can plot these points on a coordinate plane

As we can see from the plot, the four points do lie on a straight line. This is because the equation y = x/2 is the equation of a linear function with slope 1/2 and y-intercept 0. Therefore, any two points on this line will have a constant slope between them, and thus the four points will be collinear.

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The value of the sides are;

h = 2√3

c = 4√2

To determine the value, we need to note that the trigonometric identities are represented with the fraction;

sin θ = opposite /hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

From the diagram shown, we have that;

Using the sine identity

sin 60 = 3/h

Now, cross multiply the values, we have;

h = 3/sin 60

find the sine value

h = 3/√3/2

divide the values

h = 6√3/3 = 2√3

For the second triangle.

sin 45 = 4/c

cross multiply

c = 4/1/√2

c = 4√2

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Answer:

[tex]h = \boxed{2\sqrt{3}}\\\\c = \boxed{4\sqrt{2}}[/tex]

Step-by-step explanation:

We can use the law of sines to determine the sides indicated

Law Of Sines

The ratio of the sides of a triangle to the sine of the angle opposite to that side is the same for all sides

In the triangle on the leftwe have side of length 3 opposite 60° and side of length h opposite 90°

So
[tex]\dfrac{h}{\sin 90} = \dfrac{3}{\sin 60}\\[/tex]

sin 90 = 1
[tex]\sin 60 = \dfrac{\sqrt{3}}{2}[/tex]

Therefore we get
[tex]\dfrac{h}{1} = \dfrac{3}{\dfrac{\sqrt{3}}{2}}\\\\h = 3 \times \dfrac{2}{\sqrt{3}}\\\\h = \dfrac{6}{\sqrt{3}}\\\\[/tex]

Rationalizing the denominator by multiplying by √3 we get
[tex]h = \dfrac{6\sqrt{3}}{3} = \boxed{2\sqrt{3}}[/tex]  
(Answer)

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

For the triangle on the right we have
[tex]\dfrac{c}{\sin 90} = \dfrac{4}{\sin 45}\\\\\sin 90 = 1\\\sin 45 = \dfrac{1}{\sqrt{2}}\\\\c = \dfrac{4}{\dfrac{1}{\sqrt{2}}}\\\\c = 4 \times \sqrt{2}\\\\c = \boxed{4\sqrt{2}}[/tex]

(Answer)

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

In the both above computations we are using the fact that dividing by a fraction involves flipping the denominator fraction and multiplying

Answer:

first box (pies): 3, 6, 9, 12, 15, 18, 33

-> increments of 3

2nd box [cost ($)]: 11, 22, 33, 44, 55, 66, 121

-> increment of 11

Step-by-step explanation:

$44 ÷ 12 pies = $3.67 per 1 pie

3 × $3.67 = $11.01

same process: (number of pies) × $3.67 ≈ COST

Answer:

Step-by-step explanation:

So start off with 66 x 33. That will equal 2,178. Divide 2,178 by 18, like this: 2,178/18. That will equal 121. that will mean that 33 = 121. So 9 = 33 because 9 x 44 = 396 so you will divide that by 12 meaning that 9 equals 33. So now you will multiply 9 and 22 and then divide that answer by 33 making 6 = 22. now divide 22 by 6. That will equal 3.67. So 3.67 is the cost of one pie.

For the boxes above 12 and 44 it will be 16 = 59.

I hope it helped

The ratio of black and white keys of piano give correct values of A, B, C as 9, 52, 130.

The ratio of black to white keys of Piano of different sizes are as follow,

Black      A      36        63      90

White     13      B          91        C

From the table of black and white keys relation of proportionality is equal to,

( A / 13 ) = ( 36 / B ) = ( 63 / 91 ) = ( 90 / C )

This implies ,

( A / 13 ) = ( 63 / 91 )  

⇒ A = ( 63 / 91 ) × 13

⇒ A = ( 9 / 13 ) × 13

⇒ A = 9

Similarly,

( 36 / B ) = ( 63 / 91 )

⇒ B = 36 × ( 91 / 63 )

⇒ B = 36 × ( 13 / 9 )

⇒ B = 52

And

( 63 / 91 ) = ( 90 / C )

⇒ C = 90 × ( 91 / 63 )

⇒ B = 90 × ( 13 / 9 )

⇒ B = 130

Therefore, the correct values of A , B, C using the ratio of black and white keys of the piano is equal to 9, 52, 130.

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The above question is incomplete, the complete question is:

The table below shows the ratios of black to white keys on pianos of various sizes.

Black A 36 63 90

White 13 B 91 C

Determine which table has the correct values for A, B, and C.

All the trigonometric values for sin θ, cos θ and tan θ are valued below. Each trigonometric value is mentioned.

sin θ has boundaries from 0 to 1.

sin [tex]-\pi /2[/tex] = -1

sin  [tex]-\pi /3[/tex] = -0.87

sin [tex]-\pi /6[/tex] = -0.5

sin 0 = 0

sin [tex]\pi /6 \\[/tex] = 0.5

sin [tex]\pi /3[/tex] = 0.87

sin [tex]\pi /2[/tex] = 1

sin [tex]2\pi /3[/tex] = [tex]\sqrt{3}/2[/tex]

sin [tex]5\pi /6[/tex] = 1/2

sin [tex]\pi[/tex] = 1

sin [tex]7\pi /6[/tex] = -0.5

sin [tex]4\pi /3[/tex] = -0.87

sin [tex]3\pi /2[/tex] = -1

sin  [tex]5\pi /3[/tex] = -0.87

sin [tex]11\pi /6[/tex] = -0.5

sin [tex]2\pi[/tex] = 0

Similarly cos θ has boundaries.

cos [tex]-\pi /2[/tex] = 0

cos  [tex]-\pi /3[/tex] = 0.5

cos [tex]-\pi /6[/tex] = 0.87

cos 0 = 1

cos [tex]\pi /6 \\[/tex] = 0.87

cos [tex]\pi /3[/tex] = 0.5

cos [tex]\pi /2[/tex] = 0

cos [tex]2\pi /3[/tex] = -0.5

cos [tex]5\pi /6[/tex] = -0.87

cos [tex]\pi[/tex] = -1

cos [tex]7\pi /6[/tex] = -0.87

cos [tex]4\pi /3[/tex] = -0.5

cos [tex]3\pi /2[/tex] = 0

cos  [tex]5\pi /3[/tex] = 0.5

cos [tex]11\pi /6[/tex] = 0.87

cos [tex]2\pi[/tex] = 1

But tan θ has no boundaries.

tan [tex]-\pi /2[/tex] = undefined

tan[tex]-\pi /3[/tex] = -0.8

tan [tex]-\pi /6[/tex] = -1.73

tan 0 = 0

tan[tex]\pi /6 \\[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex]

tan [tex]\pi /3[/tex] = [tex]\sqrt{3}[/tex]

tan [tex]\pi /2[/tex] = undefined

tan [tex]2\pi /3[/tex] = -3

tan [tex]5\pi /6[/tex] = -0.5774

tan [tex]\pi[/tex] = undefined

tan [tex]7\pi /6[/tex] = -1.73

tan[tex]4\pi /3[/tex] = 1.73

tan [tex]3\pi /2[/tex] = undefined

tan [tex]5\pi /3[/tex] = -1.73

tan [tex]11\pi /6[/tex] = -0.58

tan [tex]2\pi[/tex] = 0

Hence, all the values mentioned in the table, were written above.

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Answer:

[tex]y - 3 = \frac{2}{3} (x - 3)[/tex]

[tex]y = \frac{2}{3} x + 1[/tex]

[tex]2x - 3y = - 3[/tex]

Step-by-step explanation:

[tex]m = \frac{ - 5 - 3}{ - 9 - 3} = \frac{ - 8}{ - 12} = \frac{2}{3} [/tex]

[tex]y - 3 = \frac{2}{3} (x - 3)[/tex]

[tex]y - 3 = \frac{2}{3} x - 2[/tex]

[tex]y = \frac{2}{3} x + 1[/tex]

[tex]3y = 2x + 3[/tex]

[tex] - 2x + 3y = 3[/tex]

[tex]2x - 3y = - 3[/tex]

Therefore, the pilot should turn by approximately 41.8 degrees to fly directly to the airport.

Trigonometry is a branch of mathematics that deals with the study of the relationships between the sides and angles of triangles. It has applications in various fields, such as engineering, physics, architecture, and astronomy. Trigonometry is based on the use of six fundamental trigonometric functions, which are sine, cosine, tangent, cosecant, secant, and cotangent. These functions are defined in terms of the ratios of the sides of a right triangle. In a right triangle, one angle is a right angle, which measures 90 degrees, and the other two angles are acute angles, which are less than 90 degrees. The three sides of a right triangle are called the hypotenuse, the adjacent side, and the opposite side. The hypotenuse is the longest side, and it is always opposite to the right angle. The adjacent side is the side that is adjacent to the angle of interest, and the opposite side is the side that is opposite to the angle of interest.

Here,

We can use trigonometry to find the angle x that the pilot should turn in order to fly directly to the airport.

First, let's draw a diagram of the situation:

A(airport)

|\

| \

|  \

|   \

|    \

|     \

|      \

|       \

|        \

|         \

|          \

P         x mi

In the diagram, P represents the position of the plane, which is 148 miles north and 167 miles east of the airport A. The line labeled "x mi" represents the distance that the plane needs to fly in order to reach the airport, and the angle x is the angle between the line x mi and the line representing the eastward direction.

To find x, we can use the trigonometric ratio for tangent (tan):

tan(x) = opposite/adjacent

In this case, the opposite side is 148 miles (the distance north of the airport) and the adjacent side is 167 miles (the distance east of the airport). Therefore:

tan(x) = 148/167

Using a calculator, we can find that:

tan(x) ≈ 0.8868

To find x, we need to take the arctangent (tan⁻¹) of both sides:

x = tan⁻¹(0.8868)

Using a calculator, we find that:

x ≈ 41.8°

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Rounding off the value of X to the nearest whole number, we get that approximately 35 people would be expected to have consumed alcoholic beverages among 50 randomly selected 18-20 year-olds.

In exercise 3.25, it was learned that about 69.7% of 18-20 year-olds consumed alcoholic beverages in 2008.

Now, consider a random sample of fifty 18-20 year-olds.

It is required to calculate the number of people who would be expected to have consumed alcoholic beverages.

Let X be the number of people who have consumed alcoholic beverages out of 50 randomly selected 18-20 year-olds.

Let p be the proportion of 18-20 year-olds who consumed alcoholic beverages in 2008.

Therefore, the sample proportion is given as \hat{p}

Hence, p=0.69 \hat{p}=X/50

Now, by the properties of the sample proportion, E(\hat{p})=p

Therefore,

E(\hat{p})=E(X/50)

Thus, p=E(X/50) Or, X=50p

Substituting the value of p, we have

X=50(0.697)=34.85

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The answer to this question is 289 miles. The sum of 89 + 73 + 127 is 289, so Julie will have driven a total of 289 miles.

Sum is the total of two or more numbers added together. It is a mathematical operation used to find the aggregate of two or more numbers or amounts. Sum is calculated by adding the numbers together to get the total.

This is because Julie will be driving a total of 89 miles from York to Derby, then 73 miles from Derby to Corby, for a total of 162 miles. She will then have to drive 127 miles from Derby back to York, giving a total of 289 miles.

Once these distances are determined, the total number of miles is simply the sum of the three distances. The sum of 89 + 73 + 127 is 289, so Julie will have driven a total of 289 miles.

To further illustrate this answer, it can be thought of as a triangle, where each location is a vertex and the lines connecting them are the distances between the locations.

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In practice, the most frequently encountered hypothesis test about a population variance is an F-test.

In statistics, hypothesis tests provide us with a tool to evaluate evidence about a population. Hypothesis testing is a crucial part of statistical inference, in which an analyst tests hypotheses using statistical methods such as t-tests, chi-squared tests, and analysis of variance (ANOVA).

In practice, the most commonly used hypothesis test for population variance is the F-test. This test can be used to test the null hypothesis that two population variances are equal. F-tests have a wide range of uses, including in quality control, financial analysis, engineering, and more. The F-test statistic is calculated by dividing the sample variance of one sample by the sample variance of another sample. The F-test requires that the data come from populations that follow normal distributions, and it is sensitive to outliers in the data.

Therefore, in practice, the most frequently encountered hypothesis test about a population variance is an F-test.

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.

One possible equation Ross can make is 9 - 7 + 8 = 10

Ross is given the numbers 6, 7, 8, and 9, and is asked to make an equation that equals 10. The equation can use each number only once, and can use any arithmetic operations (such as addition, subtraction, multiplication, and division) in any order.

One way Ross can approach this problem is to first think about what pairs of numbers can be combined to make 10. Ross could quickly see that there are no pairs of numbers that add up to 10, since the highest pair is 8 + 9 = 17.

Next, Ross could think about using subtraction or division to create a 10. However, there are no pairs of numbers that can be subtracted or divided to get 10 either.

Therefore, Ross needs to use a combination of addition, subtraction, and/or multiplication to create an equation that equals 10.

One possible equation Ross can make is:

9 - 7 + 8 = 10

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In triangle ABC as per given measurements the measure side length BC is equal to 7.26cm (Rounding to three significant figures).

In triangle ABC,

Measure of angle A = 36 degrees

Measure of angle B = 90 degrees

length of AB = 8.7cm

Use trigonometry to solve for the length of BC.

First, Measure of angle C,

In triangle ABC,

Measure of (Angle A + Angle B + Angle C ) = 180

⇒ 36 + 90 + Measure of angle C = 180

⇒ Measure of angle C = 54 degrees

Now , use the sine function to solve for BC,

sin(C) = opposite side /hypotenuse

Substitute the values we have,

⇒ sin(54) = BC/AB

⇒BC = AB × sin(54)

⇒ BC = 8.7 × 0.834

⇒ BC = 7.2558

Rounding to three significant figures, we get,

BC ≈ 7.26 cm.

Therefore, the measure of length BC in triangle ABC is equal to 7.26cm.

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The above question is incomplete, the complete question is:

ABC is a right-angled triangle. Angle B = 90. Angle A = 36. AB = 8.7 cm. Work out the length of BC. Give your answer correct to 3 significant figures.

Answer:

Step-by-step explanation:

312/520 equals 60%

other people 40%

Slope of each graph are [tex]\frac{6}{5}[/tex],[tex]\frac{-1}{3}[/tex] and 1 respectively.

Slope of a line in mathematics is defined as the ratio of the change in the y coordinate w.r.t the change in the x coordinate.

Both the change in the y-coordinate and the net change in the x-coordinate are denoted by y₂-y₁ and x₂-x₁, respectively.

Thus, the formula for the change in y-coordinate with regard to the change in x-coordinate is

m=y₂-y₁/ x₂-x₁

Taking two points as per observation

Point1: (x₁ y₁)=(0,-3)

Point2:(x₂, y₂)=(5/2,0)

Slope of line=y₂-y₁/ x₂-x₁

=[tex]\frac{0+3}{5/2-0}[/tex]

=[tex]\frac{6}{5}[/tex]

Taking two points as per observation

Point1: (x₁ y₁)=(0,3)

Point2:(x₂, y₂)=(2,2)

Slope of line=y2-y1/x2-x1

=[tex]\frac{2-3}{2-0}[/tex]

=-⅓

Taking two points as per observation

Point1: (x₁ y₁)=(-2,0)

Point2:(x₂, y₂)=(0,2)

Slope of line=y2-y1/x2-x1

=[tex]\frac{2-0}{0+2}[/tex]

=1

Hence, Slope of each graph are 6/5,-⅓ and 1 respectively.

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The population of a district in 2005 was 35,700 with a continuous annual growth rate of approximately 4%. the population in 2030 will be approximately 97,209 according to the exponential growth function.

The formula for the continuous exponential growth is given by the formula:

P = Pe^(rt)

where,P is the population in the future.

P0 is the initial population.

t is the time.

r is the continuous interest rate expressed as a decimal.

e is a constant equal to approximately 2.71828.In this problem, the initial population P0 is 35,700. The rate r is 4% or 0.04 expressed as a decimal. We want to find the population in 2030, which is 25 years after 2005.

Therefore, t = 25.We will now use the formula:

P = Pe^(rt)P = 35,700e^(0.04 × 25)P = 35,700e^(1)P = 35,700 × 2.71828P = 97,209.09.

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Answer: I got 97,042.7

Step-by-step explanation:

The vertices of polygon A'B'C'D' are A′(−0.5, 0.75), B′(−0.25, 0.25), C′(0.5, −0.25), D′(0.5, 0.5).

In geometry, dilation is a transformation that changes the size of a figure but not its shape. It is a type of similarity transformation.

When a figure is dilated, each point of the figure moves away or towards the center of dilation by a certain scale factor.

Here we have

Polygon ABCD with vertices at A(−4, 6), B(−2, 2), C(4, −2), and D(4, 4) is dilated using a scale factor of one-eighth to create polygon A′B′C′D′.

To dilate polygon ABCD using a scale factor of one-eighth i.e 1/8 multiply the coordinates of each vertex by the scale factor of 1/8.

The coordinates of A are (-4, 6), multiply each coordinate by 1/8

A' = (-4/8, 6/8) = (-1/2, 3/4) = (-0.5, 0.75)

The coordinates of B are (-2, 2), multiplying each coordinate by 1/8

B' = (-2/8, 2/8) = (-1/4, 1/4) = (-0.25, 0.25)

The coordinates of C are (4, -2), multiplying each coordinate by 1/8

C' = (4/8, -2/8) = (1/2, -1/4) = (0.5, - 0.25)

The coordinates of D are (4, 4). Multiplying each coordinate by 1/8

D' = (4/8, 4/8) = (1/2, 1/2) = (0.5, 0.5)

Therefore,

The vertices of polygon A'B'C'D' are A′(−0.5, 0.75), B′(−0.25, 0.25), C′(0.5, −0.25), D′(0.5, 0.5).

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As per the given probability, the mode of the number of hurricanes it takes for the home to experience damage from two hurricanes is either one or two hurricanes, depending on which sequence is more likely to occur.

The probability of the DD sequence is 0.4 x 0.4 = 0.16. This means that there is a 16% chance that the home will experience damage in both the first and second hurricanes.

The probability of the DN sequence is 0.4 x 0.6 = 0.24. This means that there is a 24% chance that the home will experience damage in the first hurricane but not in the second hurricane.

The probability of the ND sequence is 0.6 x 0.4 = 0.24. This means that there is a 24% chance that the home will not experience damage in the first hurricane but will experience damage in the second hurricane.

To determine the mode of the number of hurricanes it takes for the home to experience damage from two hurricanes, we need to consider which sequence is most likely to occur.

In this case, the DN and ND sequences have the same probability, which means that there are two possible modes: one and two hurricanes.

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Answer:

We can find the point that partitions line segment AB into a 3:6 ratio by using the formula for finding a point that divides a line segment into two parts in a given ratio.

Let's call the point we're looking for "P". According to the formula, the coordinates of point P can be found using the following equations:

x-coordinate of P = [(6 * x-coordinate of A) + (3 * x-coordinate of B)] / 9

y-coordinate of P = [(6 * y-coordinate of A) + (3 * y-coordinate of B)] / 9

Using the coordinates of points A and B given in the problem, we can plug them into these equations and simplify to find the coordinates of point P:

x-coordinate of P = [(6 * -1) + (3 * 2)] / 9 = 0

y-coordinate of P = [(6 * 2) + (3 * 5)] / 9 = 3.33 (rounded to two decimal places)

Therefore, the point that partitions line segment AB into a 3:6 ratio is approximately (0, 3.33), which is closest to option A: 4,5/3.

The x-intercepts of the function 3 tan(3x) over the interval (π/6, 3π/6) are:

x = π/3 and x = 2π/3

What is function ?

A function is a mathematical object that takes one or more inputs, called the arguments or variables, and produces a unique output. The output is determined by a set of rules that specify how the function operates on the inputs. In other words, a function is a relationship between inputs and outputs.

Functions are typically denoted by a symbol or a name, such as f(x) or g(t). The input is usually represented by a variable, such as x or t, while the output is represented by the function value, such as f(x) or g(t).

Functions are used extensively in mathematics, science, engineering, and many other fields. They provide a way to model and analyze real-world phenomena, and they are essential tools for solving many problems in these fields. Examples of functions include polynomial functions, exponential functions, trigonometric functions, and logarithmic functions.

To find the x-intercept of the function 3 tan(3x) over the given interval, we need to find the values of x where the function equals zero.

Let's first simplify the function:

3 tan(3x) = 0

tan(3x) = 0

We know that tan(π/2) is undefined and that tan(π) = 0. Since the period of the tangent function is π, we can say that:

tan(3x) = 0 --> 3x = nπ for n ∈ ℤ

Now we solve for x:

3x = nπ

x = nπ/3

Since the interval is (π/6, 3π/6), we need to find the values of x that satisfy:

π/6 < x < 3π/6

π/6 < nπ/3 < 3π/6

1/2 < n < 3/2

So the values of x that satisfy the given condition are:

x = π/3 and x = 2π/3

Therefore, the x-intercepts of the function 3 tan(3x) over the interval (π/6, 3π/6) are:

x = π/3 and x = 2π/3

Expressed in terms of π, the x-intercepts are:

π/3π and 2π/3π, which simplify to:

x = 1/3 and x = 2/3.

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Step-by-step explanation:

Insects can show three types of development. One of them, holometaboly (complete development), consists of the stages of egg, larva, pupa and sexually mature adult, which occupy different habitats. Insects with holometaboly belong to the most numerous orders in terms of known species. This type of development is related to a greater number of species due to the a) protection in the pupa stage, favoring the survival of fertile adults. b) production of many eggs, larvae and pupae, increasing the number of adults. c) exploration of different niches, avoiding competition between life stages. d) food intake at all stages of life, ensuring the emergence of adults. e) use of the same food in all stages, optimizing the body's nutrition.

The distance of the end of the trip from the starting point is 193.1321 km.

The ship goes 180 kilometers on bearing after 70 km of subsequent journey.

The starting point in this case is A, and the ending point is C.

We now discover distance AC:

As we can see, a right-angled triangle results.

The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two sides that make up the right angle is equal to the square of the hypotenuse. This can be expressed mathematically as a^2 + b^2 = c^2, where a and b are the two sides that make up the right angle, and c is the hypotenuse.

Use Pythagoras's principle.

c = √a² + b²

The distance in the Hypotenuse in our case is now.

c = √(70)² + (180)²

c = √4900 + 32400

c = √37,300

c = 193.1321 km

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The complete question is:

A ship travels 70 km on a bearing of 27 degrees, and then travels on a bearing of 147 degrees for 180 km. Find the distance of the end of the trip from the starting point.

The probability that the second chip drawn is red is 1/3.

The probability of drawing a red chip on the first draw is 6/10, or 3/5. After one chip is discarded, there are 9 chips remaining, 3 of which are red. So the probability of drawing a red chip on the second draw, given that a chip has already been discarded, is 3/9, or 1/3.

Therefore, the probability that the second chip drawn is red is 1/3. This is because the first chip drawn could be either white or red, so there are two possible scenarios. If the first chip drawn is white, there will be 6 red chips and 3 white chips left, so the probability of drawing a red chip on the second draw will be 6/9 or 2/3. If the first chip drawn is red, there will be 5 red chips and 4 white chips left, so the probability of drawing a red chip on the second draw will be 5/9. To get the overall probability of drawing a red chip on the second draw, we need to take the average of these two probabilities, weighted by the probability of the first chip being white or red, respectively.

The probability of the first chip being white is 4/10, or 2/5, and the probability of the first chip being red is 6/10, or 3/5. So the overall probability of drawing a red chip on the second draw is

(2/5) x (2/3) + (3/5) x (5/9) = 4/15 + 1/3 = 3/9 = 1/3.

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    the baker needs 15 gallons of milk to make 80 chocolate pies for the community festival. To translate the phrase "9r subtract three fifths greater than 3 and 9 tenths" into an expression, we first need to understand what it's asking us to do.  

  "Three fifths greater than 3 and 9 tenths" means we need to add 3 and 9 tenths to three fifths of 3. Three fifths of 3 is 1.8 (since 3/5 * 3 = 9/5 = 1.8), so we can write:

3 + 9/10 + 1.8

We can simplify this to a single mixed number by adding the whole numbers and the fractions separately:

3 + 1 + 8/10 + 8/5

= 4 + 1 3/5

= 5 3/5

So "three fifths greater than 3 and 9 tenths" is equal to 5 3/5.

Now we can subtract this value from 9r:

9r - 5 3/5

We can simplify this expression further by converting 5 3/5 to a fraction with a common denominator of 5:

9r - 5 3/5 = 9r - (28/5) = (45/5)r - (28/5) = (9r - 28) / 5

So the final expression is:

(9r - 28) / 5

In summary, "9r subtract three fifths greater than 3 and 9 tenths" can be translated to the expression (9r - 28) / 5. This expression represents a quantity that is 9 times "r" minus 5 3/5. We can simplify this expression further by converting the mixed number to an improper fraction and combining the terms, as shown above.

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The plane is approximately 44,197 feet away from the air traffic control tower.

An illustration of an angle of elevation

Between the horizontal line and the line of sight, an angle called the angle of elevation is created. When the line of sight is upward from the horizontal line, an angle of elevation is created.

Trigonometry can be used to resolve this issue. Let's illustrate:

    P (plane)

     /|

    / |

   /  |  h = altitude of plane = 5127 ft

  /   |

 / θ  |

T-----X

 d = ?

In the illustration, T stands for the air traffic control tower, P for the aircraft, for the angle of elevation, X for the location on the ground directly beneath the aircraft, and d for the desired distance.

We can see that the tower, the spot on the ground just beneath the plane, and the actual plane itself make up the right triangle TPX. The triangle's opposite and adjacent sides can be related to the angle by using the tangent function:

tan θ = h / d

where d is the desired distance and h is the plane's altitude.

To find d, we can rearrange this equation as follows:

d = h / tan θ

Inputting the values provided yields:

d = 5127 feet / 7° of tan

Calculating the answer, we obtain:

d ≈ 44,197 ft

Thus, the distance between the aircraft and the air traffic control tower is 44,197 feet.

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Answer:

Step-by-step explanation:

Given diameter of a beach ball is d=10 inches.Let us find the radius of the beach ball:d=2 r10=2×rr=102∴r=5Therefore, the radius of a beach is 5 inches.Let us find the volume of air contained inside the beach ball:V=43 π×r3=43 π×53=43 π×125=500π3∴V=523.59877Therefore, the volume of air contained inside the beach ball is approximately 523.6 in3.

Answer:

The formula for the volume of a sphere is:

V = (4/3)πr³

We can rearrange this formula to solve for the radius (r):

r = [(3V) / (4π)]^(1/3)

where V is the volume of the sphere.

Substituting the given volume of the beach ball, we get:

r = [(3 × 10,332 in³) / (4 × 3.14)]^(1/3)

r = 10.27 in

Rounding to the nearest tenth, the approximate radius of the beach ball is 10.3 inches.