Mary runs 600m every day.
Work out how far Mary runs in one week.
Give your answer in kilometres.

Therefore, it will cost $510 to carpet the hallway.

Area is a mathematical concept that describes the size of a two-dimensional surface. It is a measure of the amount of space inside a closed shape, such as a rectangle, circle, or triangle, and is typically expressed in square units, such as square feet or square meters. The area of a shape is calculated by multiplying the length of one side or dimension by the length of another side or dimension. For example, the area of a rectangle can be found by multiplying its length by its width. The concept of area is used in many fields, including mathematics, geometry, engineering, and architecture. It is an important measure for determining the amount of material needed to cover a surface, such as carpet or paint, and is used in a wide variety of real-world applications.

Here,

To find the cost of carpeting the hallway, we need to know the total area of both trapezoids in square feet. Let's assume that the trapezoids have parallel sides of length 16 and 18 feet, and a height of 6 feet.

The area of each trapezoid is given by the formula:

Area = (1/2) x (sum of parallel sides) x height

For the first trapezoid, the sum of parallel sides is 16 + 18 = 34 feet. Therefore, the area of the first trapezoid is:

Area1 = (1/2) x (16 + 18) x 6

Area1 = 102 square feet

For the second trapezoid, the sum of parallel sides is also 16 + 18 = 34 feet. Therefore, the area of the second trapezoid is:

Area2 = (1/2) x (16 + 18) x 6

Area2 = 102 square feet

The total area of both trapezoids is:

Total Area = Area1 + Area2

Total Area = 102 square feet + 102 square feet

Total Area = 204 square feet

Now that we know the area of the hallway, we can calculate the cost of carpeting it. We're told that the carpet costs $2.50 per square foot, so we can multiply the area of the hallway by the cost per square foot to find the total cost:

Total Cost = Area x Cost per square foot

Total Cost = 204 square feet x $2.50 per square foot

Total Cost = $510

To know more about area,

https://brainly.com/question/22469440

#SPJ1

Answer:

I think it's answer is no.B

Leo has 38 toy troops as there aren't enough for him to line them up four by four.

The equal symbol (=) is frequently used to separate the expressions in equations. The left-hand side (LHS) and right-hand side (RHS) of the equation, respectively, are the formulas on either side of the equal sign. If you replace the variable(s) in both expressions with the same value, they will have the same value, as indicated by the equal symbol, which denotes that the two sides are equivalent.

given

We'll name Leo's collection of toy soldiers "x" the amount.

Finally, we know that the remainder is 3 when x is split by 5. Thus, x Plus 2 must be a multiple of 5.

Using this knowledge, we can construct the following system of equations:

x = 4n (where n is a positive number) (where n is a positive integer)

x + 1 = 7m (where m is a positive number) (where m is a positive integer)

x + 2 = 5p (where p is a positive number) (where p is a positive integer)

Testing different values of x that meet these two requirements reveals that x = 38 is the only answer that also resolves the second problem.

Leo has 38 toy troops as there aren't enough for him to line them up four by four.

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

The expression 4 triangles to 16 squares when simplified is 1 triangle to 4 squares

Given that

4 triangles to 16 squares

When expressed as ratio, we have

Triangle : Square = 4 : 16

To simplify the ratio Triangle : Square = 4 : 16, we can divide both the numerator and denominator by their greatest common factor, which is 4.

So, we have

Triangle : Square = 4 : 16

Divide both sides by 4:

Triangle/4 : Square/4 = 1 : 4

So the simplified ratio is 1 : 4, which means for every one triangle, there are four squares.

Read more about ratio at

https://brainly.com/question/12024093

#SPJ1

In the following question, among the given options, the statement is said to be, The pooled estimate of the standard deviation for the data given is √(54.14^2/10 + 24.26^2/10) = 22.74.

According to the rule for examining standard deviations in ANOVA from Chapter 12 (page 560), the within-group standard deviation should be no more than twice the size of the between-group standard deviation. In this case, the between-group standard deviation is 44.85 and the within-group standard deviation (22.74) is less than twice the size of the between-group standard deviation, so it is reasonable to use a pooled standard deviation for the analysis of these data.

For more such questions on deviation

https://brainly.com/question/475676

#SPJ11

Answer:

5 less than or equal to x

Step-by-step explanation:

make x subject

Answer: profit

Step-by-step explanation:

3.95 (price of one share) multiplied by 40 (the amount of shares bought) would have cost $158. so selling all for $200 would be a $42 profit

The PC is initially worth $3,340.

Given that a computer loses half of its worth after six years, and assuming that value is $835, we must determine the device's original value.

What does the term "starting value" mean?

The starting output value is the initial value.

Let's say that computer's starting value is x.

As a result, after four years,

It is X/2 for the fourth year.

It is X/2 for the fifth year.

It's X/4 in the sixth year.

We stated that the PC will be worth $835 after six years. Hence, we may express it as,

X/4 = $835

X=4( $835)

X= $3,340

Hence, the initial value of the computer is $3,340.

To know more about initial value, click the below link

https://brainly.com/question/15004268

#SPJ4

The correct relative frequency for X is:

X: $2 $3 $4 $7

P(X): 0.38 0.15 0.28 0.19

First we need to determine the probability of each value of X occurring based on the given data.

We can use the following formula to calculate the probability of a particular value of X:

P(X = x) = f(x)/n

Where

Let's calculate the probabilities for each value of X:

P(X = $2) = 57/150 = 0.38

P(X = $3) = 23/150 = 0.15

P(X = $4) = 42/150 = 0.28

P(X = $7) = 28/150 = 0.19

Therefore, the correct relative frequency for X is:

X: $2 $3 $4 $7

P(X): 0.38 0.15 0.28 0.19

Learn more about probability here : brainly.com/question/251701

#SPJ1

The required perimeter of the trapezoid is22 units.

The given vertices of the trapezoid are (1,3), (4,7), (9,7), and (9,3). To find the perimeter of the trapezoid, we need to add up the lengths of all four sides.

We can use the distance formula to find the length of each side of the trapezoid:

[tex]{Side 1: }&(1,3) \text{ to } (4,7) \&d = \sqrt{(4 - 1)^2 + (7 - 3)^2} = \sqrt{9 + 16} = 5 \\\text{Side 2: }&(4,7) \text{ to } (9,7) \&d = \sqrt{(9 - 4)^2 + (7 - 7)^2} = \sqrt{25} = 5 \\\text{Side 3: }&(9,7) \text{ to } (9,3) \&d = \sqrt{(9 - 9)^2 + (3 - 7)^2} = \sqrt{16} = 4 \\\text{Side 4: }&(9,3) \text{ to } (1,3) \&d = \sqrt{(1 - 9)^2 + (3 - 3)^2} = \sqrt{64} = 8\end{align*}[/tex]

Therefore, the perimeter of the trapezoid is:

[tex]$\begin{align*}P &= \text{Side 1} + \text{Side 2} + \text{Side 3} + \text{Side 4} \&= 5 + 5 + 4 + 8 \&= 22\end{align*}[/tex]

Thus, the perimeter of the trapezoid is22 units.

To know more about Perimeter visit:

brainly.com/question/6465134

#SPJ1

As per the given APR, the sum of amount after 18 years is $66,373. 60, and the total deposits made over the time period is  $43,200. (option d).

To calculate this, we can use the formula for future value of an annuity:

FV = PMT x (((1 + r)⁻¹) / r)

where FV is the future value, PMT is the monthly payment, r is the monthly interest rate (which is calculated by dividing the APR by 12), and n is the number of payments (which is 18 x 12 = 216 in this case).

Plugging in the numbers, we get:

FV = $200 x (((1 + 0.045/12)²¹⁶ - 1) / (0.045/12)) = $66,373.60

Therefore, you would have approximately $66,373.60 in your investment plan after 18 years.

Now let's compare this amount to the total deposits made over the time period. In this case, the total deposits would be:

$200 x 12 x 18 = $43,200

Hence the correct option is (d).

To know more about APR here

https://brainly.com/question/14184570

#SPJ4

The researcher should reject the null hypothesis, and he can conclude the alternative hypothesis is probably correct.

The alpha level is set prior to the analysis of the data. To use the tool to identify the z-score boundaries, the user must slide the orange lines until the area in the critical region equals the alpha level. The critical region is between the two z-score boundaries. The z-score boundaries for an alpha level a = .001 are: z = 2.58 and z = -2.58, z = 1.96 and z = -1.96, z = 3.29 and z = -3.29. With an alpha of .001, the calculated z statistic of 2.64 is within the critical region. Therefore, the researcher should reject the null hypothesis, and he can conclude the alternative hypothesis is probably correct.

Learn more about Researcher

brainly.com/question/28555014

#SPJ11

Answer: x = 15

Step-by-step explanation:

Expand 1.4(x+5): 1.4x+7+1.6x = 52

Combine like terms: 3x+7 = 52

Subtract 7 from both sides: 3x = 45

Divide both sides by 3: x = 15

Answer:

The answer is x=15

Please give me Brainliest :)

1. Expand the expression

1.4x+7+1.6x=52

2. Simplify

3x+7=52

3. Separate the constants and variables

3x=52−7

4. Add or subtract numbers

3x=45

5. Divide both sides by 3

6. Simplify

x=15

Answer:

36 × 10^6 m²

Step-by-step explanation:

Given the side length of a square = 6 × 10³m,

To solve for the area of a square, use the following formula:

A = S² where:

S = side of the square

Substitute the given value for the side into the formula:

A = S²

A = (6 × 10³)²

A = 36000000 or 36 × 10^6 m²

NOTE:

6 × 10³ is also the same as 6 × 1000 = 6000,

(6 × 10³)² is essentially 6,000² = 36,000,000

Therefore, its area in square meters is 36 × 10^6

a.

There are 15,504 ways to choose 20 batteries from the given types.

b.

there are 18,564 ways to choose 20 batteries such that at least four of them are 9-volt batteries.

To choose 20 batteries from the given 5 types (aaa, aa, c, d, and 9-volt), we can use the combination formula and is given by:

nCr = n! / (r! * (n-r)!)

5C20 = 5! / (20! * (5-20)!) = 15,504

there are 15,504 ways to choose 20 batteries from the given types.

b. To choose 20 batteries such that at least four of them are 9-volt batteries, we employ the method:

First, we choose four 9-volt batteries out of the total number of 9-volt batteries, which is 1.

we then need to choose the remaining 16 batteries from the remaining 4 types (aaa, aa, c, and d), while making sure that we don't choose any 9-volt batteries.

Applying the combination formula, with n = 4 and r = 16:

4C16 = 4! / (16! * (4-16)!) = 18,564

Therefore, the total number of ways to choose 20 batteries such that at least four of them are 9-volt batteries is:

1 * 18,564 = 18,564

Learn more about combination formula at:

https://brainly.com/question/11732255

#SPJ1

Answer:

Length = 53 feet

Width = 22 feet

Step-by-step explanation:

Perimeter = 2(length + width)

Then:

a = 2w + 9            Ec. 1

150 = 2(a + w)       Ec. 2

a = length

w = width

From Eq. 1:

a - 9 = 2w            Eq. 3

From Eq. 2:

150 = 2*a + 2*w

150 = 2a + 2w

150 - 2a = 2w        Eq. 4

Equalizing Eq. 3 and Eq. 4

a - 9 = 150 - 2a

a + 2a = 150 + 9

3a = 159

a = 159/3

a = 53

From Eq. 1:

a = 2w + 9

53 = 2w + 9

53 - 9 = 2w

44 = 2w

44/2 = w

w = 22

Check:

From Eq. 2

150 = 2(a+w)

150 = 2(53+22)

150 = 2*75

Answer:

83.6%

Step-by-step explanation:

Let's say the original price is x

x decreased by 12% means 88% of x is left.

0.88x decreased by 5% means 95% of 0.88x is left.

This means the answer is: 0.88x * 0.95 = 0.836

The percent of the total decrease is 83.6%

Hope this helps :)

Have a great day!

Answer:

7

Step-by-step explanation:

x  + 3 = 10

x + 3 - 3 = 10 - 3

x = 7

As we proved that the commutator  [cA+dB. C]=c[A. C]+d[B. C] is bilinear

Let us start with the left-hand side of the equation: [cA + dB, C]. By definition, this is equal to (cA + dB)C - C(cA + dB).

Using the distributive property of multiplication, we can expand this expression to get

=> cAC + dBC - cCA - dBC.

Now let us consider the right-hand side of the equation:

=> c[A,C] + d[B,C].

By definition,

=> [A,C] = AC - CA and [B,C] = BC - CB.

Substituting these expressions into the right-hand side of the equation, we get

=> c(AC - CA) + d(BC - CB).

Using the distributive property of multiplication, we can expand this expression to get

=> cAC - cCA + dBC - dCB.

To know more about bilinear here

https://brainly.com/question/29112564

#SPJ4

Answer:

To find the population in the year 2001, we need to work backwards from the given population of 54,000 in 2003.

Let P be the population in the year 2001. From 2001 to 2003, there are two years, during which the population grows at a rate of 5% per annum. We can calculate the population in 2003 using the formula:

P * (1 + r)^n = 54,000

where r is the annual growth rate (5% or 0.05) and n is the number of years (2). Plugging in the values, we get:

P * (1 + 0.05)^2 = 54,000

Simplifying the equation, we get:

P = 54,000 / (1.05)^2

P = 48,543 (rounded to the nearest whole number)

Therefore, the population in the year 2001 was approximately 48,543.

To find the population in the year 2005, we can use the same formula with n = 2 + 2 = 4 (since we want to find the population four years after 2001):

P * (1 + 0.05)^4 = ?

Plugging in the value of P we just found, we get:

48,543 * (1 + 0.05)^4 = 60,723 (rounded to the nearest whole number)

Therefore, the population in the year 2005 would be approximately 60,723

(please could you kindly mark my answer as brainliest )

The answers for the questions given are mentioned below respectively.

In mathematics, an expression is a combination of numbers, variables, and mathematical operations that are arranged in a specific way.

It can be a single number or variable, or a combination of them, along with mathematical operations like addition, subtraction, multiplication, division, exponents, and parentheses.

8.1 - The correct expression of the form of this argument is: a. Some C are F. Some C are not S. Some S are not F.

8.2 - The substitution that proves the argument invalid is: b. C = dogs, F = animals, and S = mammals.

8.3 - The substitution that proves the argument invalid is: e. C = Abrahamm Lincoln was beheaded, F = Abraham Lincon is not dead .

8.4 - The correct expression of the form of this argument is: d. If C then F. Not C. Not F.

8.5 - The correct expression of the form of this argument is: b. All C's are A. All C that are O are the A.

8.6 - The substitution that proves the argument invalid is: c. C=men, O=married, A=husbands.

8.17 - The correct truth value of the statement is: c. Some A are B. (T)

8.18 - The correct truth value of the statement is: e. Some A are B. (T)

8.19 - The correct truth value of the statement is: a. Some non-A are B. (Und.)

To know more about mathematical operations visit:

https://brainly.com/question/8959976

#SPJ1

Answer:

To solve the problem, we need to add 23 7/8 and 3 1/2 to find the final price.

First, we need to convert 3 1/2 to an improper fraction:

3 1/2 = (2 x 3) + 1/2 = 7/2

Next, we need to find a common denominator between 8 and 2:

8 = 8/1

2 = 2/1 x 4/4 = 8/4

Now we can add the two fractions:

23 7/8 + 3 1/2

= 23 14/16 + 3 8/16 (using 16 as the common denominator)

= 27 6/16

= 27 3/8

Therefore, the stock was priced at $27 3/8 at the end of trading.

Calculating the expected value of payout using the probabilities given, we can bet on blue for all 10 races, bet on red for all 10 races and bet on purple for all 10 races

To determine the most efficient bets to increase your money during the 10 rounds, we need to consider the probability and potential payout for each racecar. We can start by calculating the expected value of each racecar's payout:

Blue: 0.3 x 2 = 0.6

Red: 0.25 x 2.5 = 0.625

Purple: 0.18 x 3 = 0.54

Yellow: 0.1 x 5 = 0.5

Black: 0.08 x 7 = 0.56

Green: 0.05 x 10 = 0.5

Orange: 0.03 x 15 = 0.45

Pink: 0.01 x 50 = 0.5

Based on the expected value of payout, the most efficient bets would be on the racecars with the highest expected value. However, we also need to consider the probability of each racecar winning or placing in the top 3.

To maximize our chances of winning, we should bet on the racecars with the highest probability of winning or placing in the top 3, even if their expected payout is not the highest.

Assuming that if one racecar is likely to win but doesn't win, they are statistically most likely to come second, and so on, we can rank the racecars in terms of their probability of winning or placing in the top 3:

1. Blue - 30% chance of winning

2. Red - 25% chance of winning

3. Purple - 18% chance of winning

4. Black - 8% chance of winning

5. Yellow - 10% chance of winning

6. Green - 5% chance of winning

7. Orange - 3% chance of winning

8. Pink - 1% chance of winning

Based on this ranking, the most efficient bets would be as follows:

1. Bet on Blue for all 10 races. The expected payout is not the highest, but the probability of winning is the highest at 30%.

2. Bet on Red for all 10 races. The probability of winning is the second-highest at 25%.

3. Bet on Purple for all 10 races. The probability of winning is the third-highest at 18%.

Betting on these three racecars will give you the highest chance of winning or placing in the top 3, and therefore, the most efficient bets to increase your money. However, keep in mind that gambling always carries risks, and there is no guarantee of winning.

Learn more on probability here;

https://brainly.com/question/24756209

#SPJ1

The vector u2 is (0, √3/3, 2/3). It is a unit vector that is orthogonal to both 8,-8,8 and 0,5,5.

Given two vectors 8,-8,8 and 0,5,5, we need to find another unit vector that is orthogonal to both the given vectors. Let's call this vector u1.The vector u1 can be obtained by taking the cross product of the two given vectors:u1 = (8,-8,8) × (0,5,5)u1 = (-40,-40,40)

To get a unit vector, we need to normalize u1 by dividing it by its magnitude:|u1| = √((-40)² + (-40)² + 40²) = 60u1 = (-40/60, -40/60, 40/60) = (-2/3, -2/3, 1/3)Now we need to find another unit vector that is orthogonal to u1.

One way to do this is to take the cross product of u1 with another vector, and then normalize the result. We can choose any vector that is not parallel to u1. For example, we can choose the vector (1,0,0).u2 = u1 × (1,0,0)u2 = (-2/3, -2/3, 1/3) × (1,0,0)u2 = (0,1/3,2/3)

To get a unit vector, we need to normalize u2 by dividing it by its magnitude:|u2| = √(0² + (1/3)² + (2/3)²) = 1/√3u2 = (0, √3/3, 2/3)

Learn more about Unit Vector

brainly.com/question/30279109

#SPJ11

Using the property of a kite: the angles formed by two unequal sides of a kite are equal. The value of ∠BCD∠BCD is

∠BCD = ∠BAD ⇒ ∠BCD = 106°  

The answer to this question is 150 adults. This is calculated by subtracting the number of boys and girls from the total number of people in the museum, 250.

Subtracting is a mathematical operation that involves the removal of one number or quantity from another. Subtracting can be done by either counting down from the larger number or counting up from the smaller number until the two numbers meet.

2/5 of 250 people is equal to 100 girls. 3/10 of 250 people is equal to 75 boys. When these two numbers are subtracted from the total number of people in the museum, 250, the answer is 150 adults.

To work out the number of adults in the museum, it is important to first identify the fractions and convert them into decimals. For example, to convert 2/5 into a decimal, 2 is divided by 5, which gives an answer of 0.4. This process should be repeated for the other fractions given in this problem.

Once the fractions are converted into decimals, the next step is to multiply the decimals by the total number of people in the museum, 250. For example, 0.4 multiplied by 250 is equal to 100 girls.

Finally, the numbers of boys and girls should be subtracted from the total number of people in the museum, 250. This gives an answer of 150 adults.

For more questions related to fractions

https://brainly.com/question/20712359

#SPJ1

By subtracting the number of boys and girls from the total number of people in the museum, we get the number of adults that is 75.

What is subtracting?

Subtracting is a mathematical operation that involves the removal of one number or quantity from another. Subtracting can be done by either counting down from the larger number or counting up from the smaller number until the two numbers meet.

2/5 of 250 people = 100 girls.

3/10 of 250 people =75 boys.

When these two numbers are subtracted from the total number of people in the museum, that is

250-(100+75)= 75 adults

Thus, the number of adults among the 250 people in a museum are 75.

For more questions related to number

https://brainly.com/question/28467694

#SPJ1

The abiotic factor that can prevent the organism from becoming preserved, AFTER it has been buried is groundwater.

An abiotic factor refers to a non-living component of an ecosystem that influences the survival and growth of living organisms.

Groundwater can cause the dissolution of minerals present in the sediment that encases the buried organism.

This process can lead to the destruction of the fossilized remains, as the minerals provide the framework for the preservation of the organism's hard parts (such as bones or shells).

Groundwater can also cause the erosion of the sediment, which can expose the buried remains and make them vulnerable to biotic factors such as scavengers, predators, and decomposers.

Predators and animals that eat bones, scavengers and plants that use the nutrients of fossils, and other animals of the same species as the organism that died are all biotic factors that can affect the preservation of the organism, but they do so before or during the burial process.

Learn more about abiotic factors on:

brainly.com/question/21333046

#SPJ1

Using the empirical rule, the percentage of the students have grade point averages that are between 1.42 and 3.7 is 99.7%

The empirical rule states that for a bell-shaped distribution, the percentage of data that lie within a specified number of standard deviations from the mean is as follows: 68% of the data lie within 1 standard deviation of the mean. 95% of the data lie within 2 standard deviations of the mean

99.7% of the data lie within 3 standard deviations of the mean. Mean = 2.56Standard Deviation = 0.38We want to know what percentage of students have a grade point average between 1.42 and 3.7. To do this, we need to convert 1.42 and 3.7 into standard deviations away from the mean.

Using the z-score formula:(1.42-2.56)/0.38 = -2.99 and(3.7-2.56)/0.38 = 3.00This tells us that a grade point average of 1.42 is about 2.99 standard deviations below the mean, and a grade point average of 3.7 is about 3 standard deviations above the mean.

Using the empirical rule, we know that 99.7% of the data lies within 3 standard deviations of the mean. So the percentage of students that have a grade point average between 1.42 and 3.7 is approximately 99.7%.Thus, the correct answer is 99.7%.

See more about standard deviations at: https://brainly.com/question/475676

#SPJ11

Refer to pic...........