Aliza needs to run at a rate faster than 8.2 feet per second in order to exceed her fastest time in a race. After running for 15 minutes, her coach determines that she is running at an average rate of 5.8 miles per hour. He converts the average rate to feet per second as shown below:



He concludes that she is not running fast enough to exceed her fastest time.

Answer:

Solution,

Let the length and breadth of smaller rectangle be l and b.

Length and breadth of larger rectangle be 3L and 3 b.

Besides, depth is same in both beds.

As area of small rectangle=180

Area of larger rectangle:

\(3l \times 3b \\ = 9lb \\ = 9 \times 180 \\ = 1620 \: kg\)

Hope this helps..

Good luck on your assignment..

Alice is 55 km from her starting point after walking a distance of 55 km along the perimeter of the park.

To find the distance Alice is from her starting point after walking along the perimeter of the park, we can use the concept of congruent sides in a regular hexagon.

The perimeter of a regular hexagon is equal to the sum of its six congruent sides. Given that each side of the hexagon is 22 km long, the total perimeter of the hexagon is 6 * 22 km = 132 km.

Since Alice walks a distance of 55 km along the perimeter of the park, we can determine the number of complete laps she makes around the hexagon by dividing the distance she walked by the perimeter of the hexagon: 55 km / 132 km = 0.4167 laps.

As Alice starts and ends at a corner of the hexagon, each complete lap brings her back to the same corner. Therefore, the fractional part of the number of laps represents the portion of the hexagon's perimeter she has traveled beyond the starting corner.

To find the remaining distance from Alice's current position to the starting point, we calculate the fractional part of the number of laps and multiply it by the perimeter of the hexagon: 0.4167 * 132 km = 55 km.

A regular hexagon is a polygon with six congruent sides. In this problem, the regular hexagon represents the shape of the park, and each side of the hexagon has a length of 22 km. The perimeter of the hexagon is found by multiplying the length of one side by the number of sides, which is 6. Therefore, the perimeter of the hexagon is 6 * 22 km = 132 km.

When Alice walks along the perimeter of the park for a distance of 55 km, we need to determine how many complete laps she makes around the hexagon. By dividing the distance she walked by the perimeter of the hexagon, we find that she completes approximately 0.4167 laps.

Since Alice starts and ends at a corner of the hexagon, each complete lap brings her back to the same corner. Therefore, the fractional part of the number of laps represents the portion of the hexagon's perimeter she has traveled beyond the starting corner.

In this case, multiplying 0.4167 by 132 km gives us a result of approximately 55 km. Therefore, Alice is 55 km from her starting point after walking a distance of 55 km along the perimeter of the park.

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To calculate the amount of soil that needs to be imported or exported in a highway construction project, we need to consider the cut and fill areas, as well as the swell and shrinkage percentages.

In this case, the cut cross sections at Stations 34+00 and 35+00 have areas of 520 and 480 square meters, respectively. The swell percentage is 20% and the shrinkage percentage is 15%.

To calculate the soil volume, we need to multiply the area by the corresponding percentage:

For Station 34+00: Cut area = 520 m², Swell percentage = 20%

Soil volume = Cut area * (1 + Swell percentage/100) = 520 m² * (1 + 20/100) = 520 m² * 1.2 = 624 m³

For Station 35+00: Cut area = 480 m², Swell percentage = 20%

Soil volume = Cut area * (1 + Swell percentage/100) = 480 m² * (1 + 20/100) = 480 m² * 1.2 = 576 m³

Since the swell percentage indicates an increase in soil volume, the soil needs to be imported to the project. The amount of soil to be imported is the difference between the calculated soil volumes and the cut areas:

Soil to be imported = Soil volume - Cut area

For Station 34+00: Soil to be imported = 624 m³ - 520 m² = 104 m³

For Station 35+00: Soil to be imported = 576 m³ - 480 m² = 96 m³

Therefore, a total of 104 cubic meters of soil should be imported at Station 34+00, and 96 cubic meters should be imported at Station 35+00 in the highway construction project.

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From the given figure , the special angle pair relationship between ∠1 and ∠3 are known as corresponding angles and are congruent.

As given in the question,

From the given figure:

line l is parallel to line m.

t is the transversal of line l and m

Relationship between angles for the parallel lines

∠1 and ∠2  are straight angles and are supplementary

∠3 and ∠2 are interior angles and are supplementary

⇒m(∠1 + ∠2) = m(∠3+∠2)

⇒m∠1= m∠3

Therefore, from the given figure , the special angle pair relationship between ∠1 and ∠3 are known as corresponding angles and are congruent.

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Answer:

angle b is 61 angle c is 58

Step-by-step explanation:

Answer:

\(24 \times \frac{1}{3} = \frac{24}{3} = 8\)

8 pupils like football

\(24 \times \frac{1}{4} = \frac{24}{4} = 6\)

6 pupils like basketball

\(24 \times \frac{3}{8} = \frac{72}{8} = 9\)

9 pupils like athletics

and how many liked swimming?

8 + 9 + 6 = 23 pupils

24-23 = 1 pupils liked swimming

GOOD LUCK ツ

4.5 is not a solution to the inequality 13 < 3x.

To check whether 4.5 is a solution to the inequality 13 < 3x, we substitute x = 4.5 into the inequality and simplify:

13 < 3x

13 < 3(4.5)

13 < 13.5

Since 13 is not less than 13.5, the inequality is not true when x = 4.5. Therefore, 4.5 is not a solution to inequality.

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The estimated volume of the Great Pyramid of Giza can be calculated using the formula for the volume of a pyramid, which is (1/3) × base area × height.

To calculate the volume of the Great Pyramid of Giza, we need to find the base area and height of the pyramid. The base of the pyramid is a square, and its dimensions are approximately 230.4 meters by 230.4 meters. To find the base area, we multiply the length of one side by itself: 230.4 m × 230.4 m = 53,046.86 square meters.

The height of the Great Pyramid of Giza is approximately 146.6 meters.

Using the formula for the volume of a pyramid, we can calculate the estimated volume of the pyramid as follows: (1/3) × 53,046.86 square meters × 146.6 meters ≈ 2,583,283 cubic meters.

Therefore, the estimated volume of the Great Pyramid of Giza is approximately 2,583,283 cubic meters.

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Answer:

Multiply the product times pi if you are leaving the answer in pi terms you can just leave the pi symbol in the answer

Hope This Helps :D

Answer:

i think the answer is y-x=15 and 25+2x=y

Answer:

yes 11 is a irrational number

Step-by-step explanation:

As we know that a decimal number that is non-terminating and non-repeating is also irrational. The value of root 11 is also non-terminating and non-repeating. This satisfies the condition of √11 being an irrational number. Hence, √11 is an irrational number.

1) After simplification: loguv + logvw + loguw -2logv - 2logu - 2logw

Given expression:

log(uv/w) + log(uw/v) + log(vw/u)- log(uvw)

Now simplify using log properties,

log(a/b) = loga - logb

log(ab) = loga + logb

Therefore,

=loguv - logw + loguw -logv + logvw - logu - logu -logv -logw

=loguv + logvw + loguw -2logv - 2logu - 2logw

Hence the simplified form is,

loguv + logvw + loguw -2logv - 2logu - 2logw

2)

Power gain \(P_{2}/ P_{1}\) = 316.22

Given,

n = 10 log(\(P_{2}/ P_{1}\))

n= 25

Now,

25/10 = \(log_{10} \frac{P_{2} }{P_{1} }\)

10^2.5 = \(P_{2}/ P_{1}\)

\(P_{2}/ P_{1}\) = 316.22 .

Hence the power gain in 316.22 .

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Answer:

137

Step-by-step explanation:

The number of ways we can choose three different numbers in order for a unique code for this case is 2730

A combination is a technique to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

We can use combinations for this case,

Total number of distinguishable things is m.

Out of those m things, k things are to be chosen such that their order doesn't matter.

This can be done in total number of ways,

⇒ \(^{m} C_{k} =\) m! / (m - k)! k!

If the order matters, then each of those choice of k distinct items would be permuted k! times.

So, total number of choices in that case would be:

⇒ \(^{m} P_{k} =\) m! / (m - k)!

This is called permutation of k items chosen out of m items (all distinct).

Given that:

The considered lock as a 3 number code

There are 15 numbers available.

None of the number can repeat.

In a lock, the order of the way numbers are arranged matters.

Because of no repetition allowed, we can simulate this situation as:

The number of ways we can choose 3 numbers out of 15 numbers with order = The number of different ways we can choose three different numbers in order for a unique code.

And we have:

The number of ways we can choose 3 numbers out of 15 numbers with order is,

⇒  \(^{m} P_{k} =\) m! / (m - k)!

⇒  \(^{15} P_{3} =\) 15! / (15 - 3)!

            = 15! / 12!

            = 2730

Thus, The number of ways we can choose three different numbers in order for a unique code for this case is 2730

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Answer:

13 weeks

Step-by-step explanation:

1,217.74 = 200.36 + 78.26w (w represents number of weeks)

Subtract 200.36

1,017.38 = 78.26w

Divide by 78.26 on both sides

w = 13

Riley will need to save money for 13 weeks to afford the new television.

I hope this helps!!

The  probability of drawing a queen, placing it back in the deck, and drawing any face card is approximately 1.78%, rounded to the nearest whole number.

Since Phil replaces the first queen back into the deck and shuffles, each draw is independent of the other. The probability of drawing a queen on the first draw is 4/52 = 1/13, and the probability of drawing a face card (other than a queen) on the second draw is 12/52 = 3/13.

The probability of both events occurring is the product of their individual probabilities:

P(drawing a queen and then a face card) = P(drawing a queen) × P(drawing a face card) = (1/13) × (3/13) = 3/169.

To express this probability as a percentage, we can multiply by 100 and round to the nearest whole number:

P(drawing a queen and then a face card) ≈ 1.78%.

Therefore, the probability of drawing a queen, placing it back in the deck, and drawing any face card is approximately 1.78%, rounded to the nearest whole number.

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Answer:

$1,763.25 X 6 = $10,579.50  

$10,579.50 X 1.045^3 = $12,072.97  

$12,072.97 - $4,360.00 = $7,712.97  

The balance after the withdrawal is $7,712.97  

Interest lost in one month is:  

$4,360.00 X 4.5% / 12 = $16.35

Answer: $16.35

The balance amount after 3 years with APR is B = $7,712.97

The annual percentage yield (APY) is the real rate of return earned on an investment, taking into account the effect of compounding interest. An APR is a number that represents the total yearly cost of borrowing money, expressed as a percentage of the principal loan amount.

Given data ,

Let the principal amount be A = $ 1,763.25

Now , the number of months n = 6 months

So , the amount in 6 months = 6 x A

The amount in 6 months = $ 10,579.50

And , the APR = 4.59 %

So , the amount after 3 years with APR = $ 10,579.50 ( 1.045 )³

The amount after 3 years with APR = $ 12,072.97

And , the withdrawal amount = $ 4,360.00

So , balance amount after 3 years with APR is B = amount after 3 years with APR - withdrawal amount

On simplifying , we get

B = $ 7,712.97

Hence,  the balance amount is B = $ 7,712.97

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The test statistic for this test is -0.213.

To test the hypothesis that two populations have the same mean, we can use a two-sample t-test. The test statistic for this test is calculated by taking the difference between the sample means and dividing it by the standard error of the difference.

In this case, the sample averages are 6 and 7, and the standard deviations for the two samples are 16 and 15, respectively. Both samples have 32 observations.

To calculate the test statistic, we first need to calculate the standard error of the difference. This is given by:

SE = sqrt[(s1^2/n1) + (s2^2/n2)]

where s1 and s2 are the standard deviations for the two samples, and n1 and n2 are the sample sizes. Plugging in the values we have, we get:

SE = sqrt[(16^2/32) + (15^2/32)]
  = 4.698

Next, we calculate the t-statistic:

t = (x1 - x2) / SE

where x1 and x2 are the sample means. Plugging in the values we have, we get:

t = (6 - 7) / 4.698
 = -0.213

The test statistic for this test is -0.213.

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The value of an depends on the exponents and the pattern of the series. By identifying the conditions that satisfy the equation, we can determine the specific values of an. The function represented by the series is an alternating series based on the pattern observed.

To determine the value of an that satisfies the equation ∑[n=1 to ∞] an xn-1 + ∑[n=0 to ∞] an xn = 0, we need to analyze the coefficients and exponents of the series.

By examining the terms in the equation, we can identify a pattern that allows us to find a solution for an. The function represented by the series ∑[n=0 to ∞] an xn can then be determined based on the values of an and the corresponding exponents.

The equation can be rewritten as ∑[n=1 to ∞] an xn-1 + an xn = 0. Notice that the terms involving xn-1 and xn have a common factor of an. Factoring out an, we get an(xn-1 + xn) = 0. For this equation to hold true for all values of x, either an = 0 or xn-1 + xn = 0.

If an = 0, then it does not contribute to the series. However, if xn-1 + xn = 0, we can solve for xn-1 = -xn. This suggests that the function represented by the series is an alternating series, where the terms alternate between positive and negative values.

In summary, the value of an depends on the exponents and the pattern of the series. By identifying the conditions that satisfy the equation, we can determine the specific values of an. The function represented by the series is an alternating series based on the pattern observed.

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The least number of seats the manger could order to 270 seats

The information that the the seats are sold only in groups of 10 will help to know that the order will be in a multiple of 10.

The manager wants to order 267 seats and this is not a multiple of 10 the nearest multiple of 10 is 270.

This is because, 260 will be short of want the manager want however ordering for 270 will be in excess with three seats.

Hence the manager will order 270 and heave 3 extra seats

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Answer:

i do not know if this will help

Step-by-step explanation:

Calculate Accrued Amount (Principal + Interest) A = Pert

Calculate Principal Amount, solve for P. P = A / ert

Calculate rate of interest in decimal, solve for r. r = ln(A/P) / t.

Calculate rate of interest in percent. R = r * 100.

Calculate time, solve for t. t = ln(A/P) / r.

Answer:

22

Step-by-step explanation:

I factor out the radicand and get 22

Let's test if my answer is correct!

22 times 22 = 484

So, my answer is correct!

Answer:

180 hours

Step-by-step explanation:

Hope this helps

A line segment has two specific endpoints in a line. The length of the line segment is set, that is the distance between two fixed points.

The length here can be measured by metric units such as centimeters (cm), and millimeters (mm), or by conventional units like feet or inches.

A closed line segment contains both endpoints, but an open line segment is exclusive of the two endpoints. A line segment that has just one endpoint is called a half-open line segment.

A line segment has two endpoints. Now if we know the coordinates of the endpoints, then we calculate the length of the line segment by distance formula.

\(D = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} -y_{1})^{2} }\)

Let a line segment has coordinates (2, –3) and (–1, –2). What is the length of a line segment?

Therefore, by distance formula,

\(D = \sqrt{(2 - (-1))^{2} + (-3 -(-2)^{2} }\)

\(D = \sqrt{(2 + 1))^{2} + (-3 +2)^{2} }\)

\(D = \sqrt{(3)^{2} + (-1)^{2} }\)

\(D = \sqrt{10}\) = 3.16

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The numbers in this problem are classified as follows:

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All the angles of the Rhombus if B-A=20 is angle A = angle C = 80°, and angle B = angle D = 100°.

In a rhombus ABCD, if angle B minus angle A equals 20 degrees (B-A=20°), we can find the degree measures of all the angles.

Step 1: Recognize that in a rhombus, opposite angles are equal. Therefore, angle A = angle C and angle B = angle D.

Step 2: Remember that the sum of the angles in any quadrilateral is 360 degrees. In a rhombus, since the opposite angles are equal, we can represent this as: 2A + 2B = 360°

Step 3: Use the given information, B - A = 20°, to solve for one of the angles. For this, rearrange the equation to isolate B: B = A + 20°

Step 4: Substitute the expression for B from step 3 into the equation from step 2: 2A + 2(A + 20°) = 360°

Step 5: Solve the equation for angle A. 2A + 2A + 40° = 360° → 4A + 40° = 360° → 4A = 320° → A = 80°

Step 6: Now that we have angle A, use the expression from step 3 to find angle B: B = 80° + 20° = 100°

Step 7: Since A = C and B = D, we can now state all the angles of the rhombus ABCD: angle A = angle C = 80°, and angle B = angle D = 100°.

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Answer:

The answer is D: 30 g.

Step-by-step explanation: I googled the answer to this question and it said that NHS reccomends that adults take around 30 g of fibre as a daily dose. If you take less, you may not get enough, but if you take more, you would possibly overdose. So, the answer is D: 30g.

Answer:

x = 2 ; y = 152

Step-by-step explanation:

15x - 2 = 9x + 10

15x - 9x = 10 + 2

6x = 12

6/6 x = 12/6

x = 2 degrees

9 * 2 + 10 + y + 180

18 + 10 + y = 180

28 + y = 180

y = 180 - 28

y = 152 degrees

The simplified form of the expression is 1.55x - 2.16.

To simplify the expression 0.2[5x + (-0.3)] + (-0.5)(-1.1x + 4.2), we can distribute the coefficients and simplify the terms.

First, distribute 0.2 to the terms inside the brackets: 0.2 * 5x + 0.2 * (-0.3) = x - 0.06.

Next, distribute -0.5 to the terms inside the second brackets: -0.5 * (-1.1x) + (-0.5) * 4.2 = 0.55x - 2.1.

Now, we can combine the simplified terms: (x - 0.06) + (0.55x - 2.1) = 1.55x - 2.16.

Thus, the simplified expression is 1.55x - 2.16.

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Answer: v=Lwh (volume = length x width x height)

Step-by-step explanation: it would be the first answer, to find volume, it’s finding the amount of space in a 3D object, kind of like area, but multiply the height to the area (bxh)

The equation of the line in slope intercept form is y = 1 / 2x - 9 / 2.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, the slope of the line is 1 / 2 and the line passes through (5, -2).

Hence,

y = 1 / 2 x + b

let's find the y-intercept using (5, -2)

Therefore,

-2 = 1 / 2 (5) + b

b = -2 - 5 / 2

b =  -4 - 5/ 2

b = -9 / 2

Therefore, the equation of the line is y = 1 / 2x - 9 / 2

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