Lydia lives 827 meters from school and 1.4 kilometers from the library. She walks to and from the school 5 days a week and walks to and from the library once a week. How many total kilometers does Lydia walk to and from the school and library each week?​

The length of r in the right triangle is 14.01 metres.

A right triangle is a triangle that has one of its angles 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, let's find the side r of the right triangle as follows:

using Pythagoras's theorem,

c² = a² + b²

where

Therefore,

r² = 6.71² + 12.3²

r² = 45.0241 + 151.29

r = √196.3141

r = 14.0112133664

r = 14.01 metres

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Step-by-step explanation:

sorry if answer is wrong

Answer:

Step-by-step explanation:

The smaller number would be 27. If the first number is 12 greater than the 2nd number and we have to make it equal to 66. Our smaller number would be 27 becuase if we add 12 to 27 that gives us 39. 39+27= 66. Hopefully that makes sense.

Answer:

x = 100/9

Step-by-step explanation:

1) Square both sides.

[tex]9x=100[/tex]

2) Divide both sides by 9.

[tex]x = \frac{100}{9}[/tex]

Decimal Form: 11.111111

1) Let [tex]x = \frac{100}{9}[/tex].

[tex]3\sqrt{\frac{100}{9} } =10[/tex]

2) Simplify [tex]\sqrt{\frac{100}{9} }[/tex] to [tex]\frac{\sqrt{100} }{\sqrt{9} }[/tex].

[tex]3\times\frac{\sqrt{100} }{\sqrt{9} }=10[/tex]

3) Since 10 x 10 = 100, the square root of 100 is 10.

[tex]3\times\frac{10}{\sqrt{9} }=10[/tex]

4) Since 3 x 3 = 9, the square root of 9 is 3.

[tex]3\times\frac{10}{3} =10[/tex]

5) Cancel 3.

10 = 10

Answer:

D. Kelly and Avery walk the same distance.

Step-by-step explanation:

Kelly walked from the 1st floor to the 5th floor. That means she walked 4 floors.
Avery walked from the 8th floor to the 4th floor.
8 - 4 = 4.
They walked the same distance, except Avery went down, and Kelly went up, which is unrelated.

Check the picture below.

[tex]\cfrac{5^2}{10^2}=\cfrac{90}{A}\implies \cfrac{25}{100}=\cfrac{90}{A}\implies \cfrac{1}{4}=\cfrac{90}{A}\implies A=360[/tex]

Answer:

21 boys

Step-by-step explanation:

girls 3+3=6+3=9+3=12+3=15+3=18+3=21

boys 2+2+2=6+2=8+2=10+2=12+2=14

3times 7=21

2 times 7 equals 14

so 21+14=35

The probability of obtaining at least one 3 or one 4 when rolling two fair dice can be calculated using complementary probability. First, find the probability of not rolling a 3 or 4 on each die, and then use this to determine the probability of the desired outcome.

For a single die, the probability of rolling a 3 or 4 is 2/6 (since there are 2 favorable outcomes out of 6 possible outcomes).

Therefore, the probability of not rolling a 3 or 4 on one die is 1 - 2/6 = 4/6 or 2/3.

When rolling two dice, the probability of not rolling a 3 or 4 on both dice is the product of their individual probabilities, which is (2/3) * (2/3) = 4/9.

Now, to find the probability of obtaining at least one 3 or one 4, we use the complementary probability:

Probability(at least one 3 or one 4) = 1 - Probability(neither die shows 3 or 4) = 1 - 4/9 = 5/9.

So, the probability of obtaining at least one 3 or one 4 when rolling two fair dice is 5/9.

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To convert kilometers per liter to miles per gallon, we need to use conversion factors. There are approximately 3.785 liters in a gallon, and there are approximately 1.609 kilometers in a mile.

So, first we convert the fuel efficiency of the hybrid vehicle from kilometers per liter to kilometers per gallon:

1 km/liter * 3.785 liters/gallon = 3.785 km/gallon

Then, we convert kilometers per gallon to miles per gallon:

3.785 km/gallon * 1 mile/1.609 km = 2.35 miles/gallon

Therefore, the gas mileage of the hybrid vehicle is approximately 2.35 miles per gallon.

It's worth noting that the mileage rating of a hybrid vehicle can vary depending on factors such as driving conditions and habits, so the actual gas mileage may differ from the stated rating. Additionally, the conversion factors used here are approximate, so the exact gas mileage may vary slightly depending on the specific conversion factors used.

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you would need to invest $1506.02 in the CD now to have $2500 for a home-entertainment center in 6 years.

The formula to calculate the future value of a simple interest investment is:

FV = P(1 + rt)

where FV is the future value, P is the principal (the initial amount invested), r is the annual interest rate (as a decimal), and t is the time period in years.

In this case, we want to find the principal that will result in a future value of $2500 in 6 years with an interest rate of 11.0% (or 0.11 as a decimal). So we can plug in the given values and solve for P:

2500 = P(1 + 0.11*6)

2500 = P(1.66)

P = 2500 / 1.66

P = $1506.02

Therefore, you would need to invest $1506.02 in the CD now to have $2500 for a home-entertainment center in 6 years.

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The base price for the ballroom rental is $295.

Tabitha is renting a ballroom for an upcoming dinner reception. The rental fee for the ballroom includes a base price plus the cost of dinner per person. The table below shows the cost of the ballroom rental in relation to the number of people attending the dinner reception.

Table showing the relation between cost and attendee.The table shows that if 20 people attend, the total rental cost will be $455, and if 60 people attend, the total rental cost will be $775. Therefore, the increase in cost from 20 attendees to 60 attendees is $320. Thus, the difference between the cost for 20 attendees and the base price is $455 - (20 * cost of dinner per person), and the difference between the cost for 60 attendees and the base price is $775 - (60 * cost of dinner per person).Let b be the base price and c be the cost of dinner per person.

Therefore,

455 - (20c) = band775 - (60c) = b Subtracting the first equation from the second equation gives:

775 - (60c) - [455 - (20c)] = b320 = 40c, Therefore, c = 8.Substituting c = 8 into either of the equations above, we can find b:455 - (20c) = 455 - (20 * 8) = 295.

Therefore, the base price for the ballroom rental is $295.

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Probability of

=0.0403.

The probability that exactly two of the 14 students selected with replacement will wear wrist watches is 3/30 * 2/29 * 27/28 * 26/27 = 0.0437.

The probability that exactly two of the 14 students selected without replacement will wear wrist watches is 3/30 * 2/29 * 26/28 * 25/27 = 0.0403.

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The inequality to represent this situation is T < 15°C, where T is the temperature.

Inequality is a statement that two values, expressions, or quantities are not equal. Inequality is usually represented by the symbols ">", "<", "≥", or "≤".

This inequality can be graphed on the number line by representing 15°C as a point on the number line. Any values to the left of 15°C, such as 14°C, 13°C, and so on, would be represented as points to the left of 15°C on the number line.

Less than inequality is used to compare two values ​​to see if one is less than the other. In this case, the inequality T < 15°C states that the temperature T must be less than 15°C in order for the furnace to turn on.

Graphically, the solution to this inequality is represented by a number line with a point at 15°C and all points to the left of 15°C represented in the solution set.

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a pie chart would be an effective way to quickly and easily understand the distribution of time spent on different course subjects.

For visualizing the percentage distribution of different course subjects, a pie chart would be the most suitable type of chart. Pie charts are ideal for displaying the relative proportions of different categories or groups as slices of a circular pie. Each slice of the pie represents a proportion of the whole, which in this case would be the total time spent on all course subjects during homework sessions. The size of each slice will correspond to the percentage of time spent on each course subject. Therefore, a pie chart would be an effective way to quickly and easily understand the distribution of time spent on different course subjects.

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Yes, this relation is a function and here the domain and range are:

domain = {3,6,2,-7} and range ={0,-2,-1,0}

Domain and Range:

The domain and scope of a function are part of the function. The domain is the set of all input values ​​of a function, and the range is the possible outputs given by the function. Field → Function → Sequence. If there is a function f : A → B such that each element of set A corresponds to an element of set B, then A is the field and B is the codomain. The graph of an element "a" under a relation R is given by "b", where (a,b) ∈ R.

The scope of the function is the set of images. The domain and range of a function are usually expressed as:

Domain(f) = {x ∈ R: State} and range(f)={f(x): x ∈ domain(f)}

According to the Question:

The given function is:

{(3,0),(6,-2),(2,-1),(-7,0)}

It is a function as every input has a single output.

So, 3,6,2,-7 are the elements of the domain of the given relation.

Here domain = {3,6,2,-7} and range ={0,-2,-1,0}

Therefore, this relation is a function.

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Answer:10root6

Step-by-step explanation:

To balance the equation, the right side of the equation must also change by 4%.

What is equation?

An equation is a mathematical statement that asserts the equality of two expressions. It consists of two sides, a left-hand side (LHS) and a right-hand side (RHS), separated by an equals sign (=)

To balance the exchange equation, the percentage change on the left side of the equation [tex](\% \triangle M + \% \triangle V)[/tex] must equal the percentage change on the right side of the equation [tex](\% \triangle P + \% \triangle Q)[/tex].

Given that there has been a 3% change in the money supply [tex](\% \triangle M)[/tex] and a 1% change in velocity [tex](\% \triangle V)[/tex], the left side of the equation can be written as:

[tex]\%\triangle M + \%\triangle V = 3\% + 1\% = 4\%[/tex]

To balance the equation, the right side of the equation must also change by 4%. Therefore, the correct answer is:

B. 4%

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The depth of water in a tank oscillates once every 6 hours, with a smallest depth of 5.5 feet and a largest depth of 8.5 feet. This can be expressed in a formula as a function of time in hours. The formula is: Depth = 5.5 + (3/2) * sin(2πt/6)

The formula is: Depth = 5.5 + (3/2) * sin(2πt/6), where t is the time in hours. This formula expresses the oscillating nature of the water level, which ranges from 5.5 to 8.5 feet. The sine function used in the formula reflects the oscillation of the depth. The frequency of the oscillation is determined by the factor (2πt/6) and the range is determined by the amplitude (3/2).
To better understand this formula, consider the example of a tank with a depth of 5.5 feet when the time is 0 hours. After 6 hours, the time has increased to t = 6 and the formula yields a depth of 8.5 feet. This shows that the formula is correctly representing the oscillation of the water level, with an amplitude of 3/2.

To summarize, the formula for the depth of water in a tank oscillating once every 6 hours with a smallest depth of 5.5 feet and a largest depth of 8.5 feet is given by the expression Depth = 5.5 + (3/2) * sin(2πt/6). This formula incorporates a sine function with a factor (2πt/6) and an amplitude of 3/2. The factor determines the frequency of the oscillation, while the amplitude determines the range of the oscillation.

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Step-by-step explanation:

75+42=117

180-117=63

Three of same angles makes the congruent triangles :)

If the first and last pages of a document must be printed in color, and only two printers can print in color, then there are a total of 4⁹⁹ ways that 100 pages can be assigned for printing to four printers.

The fundamental principle of counting says that if there are p ways to do one thing and q ways to do another thing, then there are p×q ways to do both things. Number of printers that is able to print in color = 2

Number of colors printed by printers = 2

We have to determine the number of ways are there for the 100 pages to be assigned to the four printers. Now, consider there are no restrictions. Let's break this problem into two parts. First, we have to print 2 pages in color and there are only two color printers. So, number of ways to print the first and the last page of the document = 2²

= 4

Number of remaining pages of document = 98

Number of avaliabile printers = 4

Now, second part, we have only 98 pages (out of 100 pages, 2 colors pages are already printed). Each of these 98 pages can be assigned to a printer in 4 ways. So, number of ways to print remaining 98 pages of document = 4⁹⁸.

Using the counting principle, number of ways for printing the 100 pages by four printers = 2² × 4⁹⁸

= 4 × 4⁹⁸ = 4⁹⁹

Hence, required number of ways are 4⁹⁹.

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From the given information provided, the area of the deck Edgar built in his backyard is 192 square feet.

The area of rectangular section is :

Area of rectangle = length x width

Substituting the given values, we get:

Area of rectangle = 16 ft x 8 ft

Area of rectangle = 128 square feet

The area of square section is :

Area of square = side x side

Substituting the given value, we get:

Area of square = 8 ft x 8 ft

Area of square = 64 square feet

Therefore, the total area of the deck is the sum of the area of the rectangular section and the area of the square section:

Total area of deck = Area of rectangle + Area of square

Total area of deck = 128 square feet + 64 square feet

Total area of deck = 192 square feet

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The surface area of the cylinder with radius 5 inches and rectangle with height 4 inches is equal to 282.6 square inches.

Radius of the base = 5 inches

Height of the rectangle = 4 inches

Surface area of a cylinder

= area of the top and bottom circular faces + the area of the curved surface.

Here,

Rectangle represents the curved surface of the cylinder, with a height of 4 inches and a length equal to the circumference of the base.

Circumference of the base is equal to,

Circumference

= 2πr

= 2 x 3.14 x 5

= 31.4 inches (approx.)

Area of the curved surface of the cylinder is ,

Curved surface area

= Length x Height

= 31.4 inches x 4 inches

= 125.6 square inches

Area of each circular face of the cylinder is ,

Circular face area

= πr²

= 3.14 x 5²

= 78.5 square inches

Substitute the value to get total surface area of the cylinder we have,

Total surface area of the cylinder

= 2 x Circular face area + Curved surface area

= 2 x 78.5 square inches + 125.6 square inches

= 282.6 square inches (approx.)

Therefore, the surface area of the cylinder is approximately equal to 282.6 square inches.

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Answer:

B. y less than or equal to - 2x + 1

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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.

Answer:

There are a total of 143 + 62 = 205 people coming to the party.

To calculate the number of tables needed, we divide the total number of people by the number of people per table:

205 ÷ 15 = 13 with a remainder of 10

Since we can't have a fraction of a table, we need to round up to the nearest whole number, which means the Saad family will need 14 tables for all guests.

The percent of error of Mc Doogles is 2.8%

To calculate the percent of error, we need to find the absolute difference between the expected value and the actual value, divide that by the expected value, and then multiply by 100 to get a percentage.

Given that:

Absolute difference = | 1200 - 1166 | = 34

Now:

Percent of error = (Absolute difference / Expected value) x 100

Percent of error = (34 / 1200) × 100%

Percent of error = 2.8%

Therefore, the percent of error is 2.8% (rounded to the nearest tenth of a percent).

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The volume of the container is 91125 cubic meters.

What is volume?

A measurement of three-dimensional space is volume. It is frequently expressed numerically using SI-derived units, as well as different imperial or US-standard units. Volume and the definition of length are related.

A sphere is the most basic and typical form of a three-dimensional shape. A sphere's radius is the simplest parameter to measure. The radius of the sphere is used to determine its volume.

Given the edge of a cube is 45 meters.

The formula of volume is V = s³.

The volume of the container is

45³

= 91125 cubic meter.

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Answer:

y = 43

Step-by-step explanation:

Given AB is a straight line segment, and since angles on a straight line sum to 180°, we can construct the following equation:

⇒ 47° + y° + 90° = 180°

To find the value of y, solve the equation for y:

⇒ 137° + y° = 180°

⇒ 137° + y° - 137° = 180° - 137°

⇒ y° = 43°

⇒ y = 43

Therefore, the value of y is 43.

Max has approximately 111 friends on January 1st of the next year.

Given that Max has 30 friends on January 1st, the number of friends increases by 21% every month.

We need to find out how many friends Max has on January 1st of the next year,

which is 12 months later.

First, we will calculate the number of friends Max has after one month: 30 + (21% of 30) = 30 + 0.21*30 = 36So, after the first month, Max has 36 friends.

Now, we will calculate the number of friends Max has after two months: 36 + (21% of 36) = 36 + 0.21*36 = 43.56 ≈ 44So, after the second month, Max has 44 friends.

Similarly, we can calculate the number of friends Max has after 12 months:30 + (21% of 30) + (21% of 30) + ... (12 times)≈ 30 + 6.3 + 7.65 + ... (12 terms)≈ 111.1

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The amount of concrete needed to make the stairs that leads to the garage is 64 cubic feet

The missing information is added as an attachment

The concrete needed to make the stairs is the volume of the stairs and this is calculated using

Volume = Base area * Height

Where

Base area = 3 * 2 + 2 * 1

Base area = 8

And

Height = 8

So, we have

Volume = 8 * 8

Evaluate

Volume = 64

Hence, the amount needed is 64 cubic feet

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