2) After fuel prices rose by 15%, a
family's annual heating bill was £1654.
What would the bill have been without
the price increase?

The correct option for the past forecasts using the 2-period moving average method is:
A. F1 = 5582 F2 = 5352 F3 = 5438.5 F4 = 6037.5 F5 = 5736.5

Step-by-step explanation:
1. To calculate F2, take the average of Period 1 and Period 2 actual sales: (5582 + 5122) / 2 = 5352.
2. For F3, average Period 2 and Period 3 actual sales: (5122 + 5755) / 2 = 5438.5.
3. For F4, average Period 3 and Period 4 actual sales: (5755 + 6320) / 2 = 6037.5.
4. For F5, average Period 4 and Period 5 actual sales: (6320 + 5153) / 2 = 5736.5.

"Random variation" encompasses the irregular changes in a time series that are not caused by any other component. Some  common example of random variation is coin toss. It  is independent of the effects of systematic biases. In general, the larger the sample size is, the lower the random variation is of the estimate of a parameter. As random variation decreases, precision increases.

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Thus, the two positive whole numbers that are greater than one multiply to 576 and share only the number one in common is 5.

One of the categories that mathematicians have created for numbers is titled whole numbers, and it contains all of the numbers from 0 to infinity.

The specific class or collection of numbers known as whole numbers includes:

Two positive whole numbers greater than 1 are 2 and 3.

2 and 3 does not have any common factor except 1.

sum of 2 and 3 = 5

Thus, the two positive whole integers that are greater than one multiply to 576 and share only the number one in common is 5.

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15 divided by 289 is approximately equal to 0.0519 or 519/10000. Fifteen divided by two hundred and eighty nine is a division problem that involves dividing 15 by 289. To solve this problem, we can use long division or a calculator.

Using long division, we start by dividing the first digit of the dividend (2) by the divisor (15). Since 2 is less than 15, we add a decimal point and a zero to the dividend and continue the process. We bring down the next digit (8) and divide 28 by 15, which gives us a quotient of 1 with a remainder of 13. We add a decimal point after the quotient and bring down the next digit (9) to get 139 as the new dividend. We divide 139 by 15, which gives us a quotient of 9 with a remainder of 4. We add a decimal point after the quotient and bring down the last digit (0) to get 40 as the new dividend. We divide 40 by 15, which gives us a quotient of 2 with a remainder of 10. Finally, we add a decimal point after the last quotient and write the remainder as a fraction over the divisor to get the final answer:

15 divided by 289 is approximately equal to 0.0519 or 519/10000.

In summary, fifteen divided by two hundred and eighty nine is a division problem that can be solved using long division or a calculator. The answer is a decimal or a fraction, depending on how the division is carried out.

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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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Answer:

2072

Step-by-step explanation:

Multiply 14 x 37

518 x 4

2072

Answer: $2,072 a month

Step-by-step explanation:

multiply 14 by 37 to see her weekly rate which is $518 a week. then multiply  518 by 4 (because there are about 4 weeks in a month). then you get the answer of $2,072

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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Step-by-step explanation:

Mathematics for Social Science 1011 PDF

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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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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.

Triangle ABC is similar to triangle DEF. The tangent of angle A is equal to 5/12 and the sine of angle F is 1/13.

The sine of the angle is the proportion of a right-angled triangle's hypotenuse to its perpendicular.

Triangle ABC and triangle DEF are similar in that their respective sides are proportional and their corresponding angles are equal. As a result, we have:

BC/EF = AC/DF = AB/DE

To determine the ratio AB/BC, we can utilise the tangent of angle A:

Tan(A) = 5/12 = AB/BC

By multiplying both sides by 12, we may make this simpler:

AB/BC = 12 tan(A).

We can now determine the ratio AB/EF using the ratio BC/EF:

AB/DE = BC/EF

This can be rearranged to yield AB/EF:

BC/EF * DE/AB = AB/EF

Due to the similarity of the triangles, we know that BC/EF = 12/13 and can therefore insert this into the equation:

(12/13) * (AB/DE) = AB/EF

Using the formula AB/DE = 5/12 (from above), we can reduce this:

AB/EF = (12/13) * (5/12) = 5/13

Finally, we may calculate the sine of angle F using the sine ratio:

sinning(F) = EF/DF

Using the ratio AB/EF that we recently discovered, we may rephrase this as follows:

sin(F) = (1/AB) * (AB/EF) = (1/AB) * (5/13)

Simplifying and substituting AB = 5k results in:

sin(F) is equal to (1/5k) x (5/13) x 1/(k*13).

We can select k = 1 because we want the response in its simplest form:

sin(F) = 1/13

As a result, 1/13 is the sine of angle F.

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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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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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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 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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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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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:

18.29 x 10^12

Step-by-step explanation:

you can simplify the answer as needed

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.

Answer:

18

Step-by-step explanation:

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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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:

312/520 equals 60%

other people 40%

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

Based on the information in the image, we can infer that the surface area is 863.5cm³.

To find the surface of the figure we must divide the figure in two, into the cone and the cylinder and find the surface of each one separately and then add it.

Cylinder surface area:

To calculate the surface area of a cylinder we must apply the following formula:

[tex]A = 2\pi r h ++ 2 \pi r^{2} \\A = 2 * \pi * 5 * 15 + 2 * \pi * 5^{2} \\A = 471 + 157\\A = 628cm^{3}[/tex]

Cone surface area:

[tex]A = \pi rh + \pi r^{2} \\A = \pi * 5 * 10 + \pi * 5^{2} \\A = 157 + 78.5 \\A = 235.5 cm^{3}[/tex]

Surface area of the entire figure:

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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

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 airplane's average rate in calm air is 600 mph.

What is an average?

In mathematics, the average is a measure of the central tendency of a set of numerical values, which is computed by adding all the values in the set and dividing them by the total number of values. The average is also known as the mean, and it is one of the most commonly used measures of central tendency in statistics

Let's denote the airplane's average rate in calm air by x mph.

When the airplane is flying with the jetstream, its ground speed (speed relative to the ground) is x + 300 mph. We know that it can fly 3000 miles in the same amount of time it takes to fly 1000 miles against the jetstream, so we can set up the following equation:

3000 / (x + 300) = 1000 / (x - 300)

We can cross-multiply to simplify:

3000(x - 300) = 1000(x + 300)

Expanding the brackets gives:

3000x - 900000 = 1000x + 300000

Simplifying and rearranging terms gives:

2000x = 1200000

x = 600

Therefore, the airplane's average rate in calm air is 600 mph.

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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 average value of a necklace at Julie's shop is $4.90. For further explanation;-

Julie the jeweler has two gold necklaces worth $105, seven silver necklaces valued at $100, twenty-seven plated necklaces valued at $55, and twenty-two beaded necklaces worth $25. The average value of a necklace at Julie's shop can be calculated by finding the sum of the values of all the necklaces and dividing it by the total number of necklaces.

The total value of all the necklaces is $105 + $100 + $55 + $25 = $285. The total number of necklaces is 2 + 7 + 27 + 22 = 58.

Therefore, the average value of a necklace is $285 / 58 = $4.90. This answer should be rounded to the nearest cent, giving an average value of $4.90 per necklace at Julie's shop.

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The p-value is (0.0297)

To test the hypothesis that jumping does not affect the girls' breath-holding times, we will conduct a paired t-test using the given data. Here's a step-by-step explanation:

Solution:

1. Calculate the difference between relaxed and jumping times for each girl:
(27-20), (49-43), (31-28), (22-21), (23-25), (45-43), (37-35), (29-32)
The differences are: 7, 6, 3, 1, -2, 2, 2, -3

2. Compute the mean and standard deviation of the differences:
Mean = (7+6+3+1-2+2+2-3)/8 = 16/8 = 2
Standard Deviation = sqrt[((7-2)^2+(6-2)^2+(3-2)^2+(1-2)^2+(-2-2)^2+(2-2)^2+(2-2)^2+(-3-2)^2)/7] = sqrt(42/7) = sqrt(6)

3. Calculate the t-statistic:
t = (Mean - Hypothesized Mean) / (Standard Deviation / sqrt(N))
t = (2 - 0) / (sqrt(6) / sqrt(8)) = 2 / (sqrt(6) / 2.828) ≈ 2 / 0.748 ≈ 2.675

4. Determine the p-value using the t-distribution table or calculator for a two-tailed test with 7 degrees of freedom (N-1) at the 5% level:
The p-value is 0.0297 (rounded to four decimal places).

Since the p-value (0.0297) is less than the significance level of 0.05, we reject the null hypothesis that jumping does not affect the girls' breath-holding times, on average.

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